delete all files not useful to complex calculation
This commit is contained in:
Florian Stecker
parent
1a85a5ef14
commit
3309c37955
41
barbot.plt
41
barbot.plt
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@ -1,41 +0,0 @@
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set size ratio 1.3
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set grid
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set xrange [1/2.5:2.5]
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set yrange [0.2:5]
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set samples 2000
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set parametric
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set log x
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set log y
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set terminal pngcairo size 1000, 1200
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set output "barbot-symmetric.png"
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# solves the equation rho(s)q^2 - (s+1)q + 1 = 0
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# (s^2 + cs + 1)q^2 - (s+1)q + 1 = q^2 s^2 + (cq - 1)qs + (q^2 - q + 1)
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c = 2*cos(4*pi/5)
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rho(s) = s**2 + c*s + 1
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# qp(s) = (s+1+sqrt((s+1)**2 - 4*rho(s)))/(2*rho(s))
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# qm(s) = (s+1-sqrt((s+1)**2 - 4*rho(s)))/(2*rho(s))
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# d(q) = q**2*(c*q-1)**2 - 4*(q**2-q+1)*q**2
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# sp(q) = (-(c*q-1)*q + sqrt(d(q)))/(2*q**2)
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# sm(q) = (-(c*q-1)*q - sqrt(d(q)))/(2*q**2)
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qp(s) = (s+1+sqrt((s+1)**2 - 4*rho(s)))/(2*sqrt(rho(s)))
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qm(s) = (s+1-sqrt((s+1)**2 - 4*rho(s)))/(2*sqrt(rho(s)))
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d(q) = q**2*(c*q-1)**2 - 4*(q**2-q+1)*q**2
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sp(q) = (-(c*q-1)*q + sqrt(d(q)))/(2*q**2)
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sm(q) = (-(c*q-1)*q - sqrt(d(q)))/(2*q**2)
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plot "output/barbot_map_5000_frequencies" \
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using ($1/100.0):($2/100.0*sqrt(rho($1/100.0))):(($3==0)?1/0:$4) w p pt 5 ps 0.5 lc palette t '', \
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"output/barbot_map_500000" \
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using ($1/10.0) :($2/10.0*sqrt(rho($1/10.0))) :($3*0.7+0.3) w p pt 7 ps variable lc 3 t '', \
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sm(t), d(t) > 0 ? t*sqrt(rho(sm(t))) : 1/0 w l lw 2 lc 7 t "", \
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sp(t), d(t) > 0 ? t*sqrt(rho(sp(t))) : 1/0 w l lw 2 lc 7 t "", \
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t, qm(t) w l lw 2 lc 7 t "", \
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t, qp(t) w l lw 2 lc 7 t ""
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# plot "output/barbot_map_50000_zoom_b" using ($1/1000.0):($2/5000):(($3==0)?1/0:$4) w p pt 5 ps 0.5 lc palette t ''
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# pause mouse keypress
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# reread
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BIN
billiard.pdf
BIN
billiard.pdf
Binary file not shown.
BIN
billiard.xopp
BIN
billiard.xopp
Binary file not shown.
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@ -1,31 +0,0 @@
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#!/bin/bash
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trap 'exit 130' INT
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wordlength=30
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sdenom=1
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sstart=1
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send=1
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qdenom=100
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qstart=1
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qend=200 # 1/sqrt(2) = 0.7071...
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words="$(./billiard_words $wordlength | awk '{print $1}')"
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#words="cbabcabacabcacbcab cabacabcacbcabcbab cabcacbcabcbabcaba"
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#words="abcabc abcb cbabcacbcacbab"
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#words="abcabc abcbcabcbc"
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#words="abcabc bcbab bcbabcac"
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for s in $(seq $sstart $send); do
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for q in $(seq $qstart $qend); do
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i=0
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echo -n "$s/$sdenom $q/$qdenom "
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# MAXIMUM=only ./special_element $s/$sdenom $q/$qdenom $words
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# MAXIMUM=no ./special_element $s/$sdenom $q/$qdenom abcb
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MAXIMUM=no ./special_element $s/$sdenom $q/$qdenom $words | while read line; do
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echo -n "$line "
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((i=i+1))
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done
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echo
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done
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done
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@ -1,62 +0,0 @@
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import Data.List
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import Data.Ord
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import Text.Printf
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import System.Environment
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main = do
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argv <- getArgs
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listWordsUpToLength $ read $ argv !! 0
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listWordsUpToLength :: Int -> IO ()
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listWordsUpToLength n = do
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putStr $ unlines [printf "%s %d/%d %f"
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w
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(p `div` gcd p q)
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(q `div` gcd p q)
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(atan (sqrt 3 / (2*q_/p_ + 1))) |
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((p,q),w) <- wordlist (n `div` 2, n `div` 2),
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let p_ = fromIntegral p :: Double,
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let q_ = fromIntegral q :: Double,
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length w <= n,
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let x = 2*q + p,
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let y = 2*p + q]
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-- (sqrt 3 / 2 * fromIntegral p / (fromIntegral q + fromIntegral p / 2) :: Double) |
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-- (slopeWord "bca" (orthogonalSlope (p,q))) |
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wordlist :: (Int,Int) -> [((Int,Int),String)]
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wordlist (pmax,qmax) = nub $
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sortBy (comparing sl)
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[((p `div` gcd p q, q `div` gcd p q), slopeWord "bca" (p,q)) |
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p <- [0..pmax],
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q <- [0..qmax],
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q /= 0] -- use p /= 0 || q /= 0 for more symmetric output
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where
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sl ((p,q),_) = fromIntegral p / fromIntegral q
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-- letters: reflection along e_1, reflection along e_2, other one; p,q >= 0
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-- the "slope" (p,q) means the Euclidean vector q*e_1 + p*e_2, where e_1,e_2 are at a 60 degree angle
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-- in Euclidean coordinates this is (q + p/2, sqrt(3)/2 * p)
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slopeWord :: [Char] -> (Int,Int) -> String
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slopeWord [x,y,z] (p,q)
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| p > q = slopeWord [y,x,z] (q,p)
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| otherwise = concat $ map word $ zipWith step list (tail list)
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where
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p_ = p `div` gcd p q
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q_ = q `div` gcd p q
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xmax = if (p_-q_) `mod` 3 == 0 then q_ else 3*q_ :: Int
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list = [(x,(x*p) `div` q) | x <- [0..xmax]]
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step (x1,y1) (x2,y2) = ((x1-y1) `mod` 3, y2-y1)
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word (0,0) = [z,x]
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word (1,0) = [y,z]
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word (2,0) = [x,y]
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word (0,1) = [z,y,x,y]
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word (1,1) = [y,x,z,x]
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word (2,1) = [x,z,y,z]
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-- assuming p, q >= 0
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orthogonalSlope :: (Int, Int) -> (Int, Int)
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orthogonalSlope (p,q)
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| p > q = (p-q, p+2*q)
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| p < q = (q+2*p, q-p)
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| otherwise = (1,0)
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57
cdf.plt
57
cdf.plt
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@ -1,57 +0,0 @@
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#if(!exists("logt")) logt = log(1.80)
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if(!exists("n")) n = 263
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if(!exists("logt")) logt = log(1)
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if(!exists("logs")) logs = log(1)
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#logt = 0.01*n
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logt = log(1000000000)
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file = sprintf("< ./singular_values 713698 %f %f", exp(logs), exp(logt))
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#file = sprintf("< ./singular_values 1621 %f %f", exp(logs), exp(logt))
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#outfile = sprintf("cdf/cdf_hires_%05d.png", n)
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outfile = sprintf("cdf/cdf_hires_limit.png")
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set log x
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set zeroaxis
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set samples 1000
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set size square
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set xrange [0.5:2]
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set yrange [0:500000]
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#set yrange [0:1000]
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set trange [0:30]
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set grid
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set parametric
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set terminal pngcairo enhanced size 1024, 1024
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set output outfile
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print sprintf("n = %d, t = %.2f", n, exp(logt))
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# plot file using 2:3 w p pt 7 ps 0.5 lc 1 t title
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#tr(a,b) = exp((2*a+b)/3) + exp((b-a)/3) + exp(-(a+2*b)/3)
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#trinv(a,b) = exp(-(2*a+b)/3) + exp((a-b)/3) + exp((a+2*b)/3)
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tr(a,b) = exp(a) + exp(b-a) + exp(-b)
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trinv(a,b) = exp(-a) + exp(a-b) + exp(b)
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#plot file using 6:7 w p pt 7 ps 0.5 lc 1 t columnheader,
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# log(tr(t,t*2)),log(trinv(t,2*t)) w l lw 2 t "", \
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# log(tr(t,t/2)),log(trinv(t,t/2)) w l lw 2 t ""
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plot file using 8:3 w steps lw 2 lc 1 t sprintf("t = %.2f", exp(logt))
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#plot for[i=-10:10] log(tr(t,t*exp(log(2)*i/10.0))),log(trinv(t,t*exp(log(2)*i/10.0))) w l lw 2 t ""
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#plot for[i=-10:10] t,log(tr(t,t*exp(log(2)*i/10.0)))-t w l lw 2 t ""
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##plot for[i=20:20] t,log(tr(1/t,exp(2*log(2)*i/20.0-log(2)))) w l lw 2 t ""
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#n=n+1
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#if(n < 1000) reread
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# pause mouse keypress
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# if(MOUSE_KEY == 60) logt=logt-0.02
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# if(MOUSE_KEY == 62) logt=logt+0.02
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# if(MOUSE_KEY == 44) logs=logs-0.02
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# if(MOUSE_KEY == 46) logs=logs+0.02
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# if(MOUSE_KEY != 113) reread
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@ -1 +0,0 @@
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ffmpeg -f image2 -framerate 20 -i test%03d.png -s 1024x1024 -c:v libvpx-vp9 -lossless 1 test.webm
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353
linalg.c
353
linalg.c
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@ -1,353 +0,0 @@
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#include <stdio.h>
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#include <stdlib.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_eigen.h>
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#include <gsl/gsl_blas.h>
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#include <gsl/gsl_linalg.h>
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#include <gsl/gsl_complex_math.h>
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#include <memory.h>
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#include <math.h>
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#include "linalg.h"
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#define ERROR(condition, msg, ...) if(condition){fprintf(stderr, msg, ##__VA_ARGS__); exit(1);}
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#define FCMP(x, y) gsl_fcmp(x, y, 1e-10)
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/*********************************************** temporary storage ********************************************************/
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workspace_t *workspace_alloc(int n)
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{
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workspace_t *result = (workspace_t*)malloc(sizeof(workspace_t));
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result->n = n;
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result->work_nonsymmv = gsl_eigen_nonsymmv_alloc(n);
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result->work_symmv = gsl_eigen_symmv_alloc(n);
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result->work_sv = gsl_vector_alloc(n);
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result->eval_complex = gsl_vector_complex_alloc(n);
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result->evec_complex = gsl_matrix_complex_alloc(n, n);
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result->eval_real = gsl_vector_alloc(n);
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result->evec_real = gsl_matrix_alloc(n, n);
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result->permutation = gsl_permutation_alloc(n);
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result->tmp_mat = malloc(MAX_TEMP_MATRICES*sizeof(gsl_matrix*));
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for(int i = 0; i < MAX_TEMP_MATRICES; i++)
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result->tmp_mat[i] = gsl_matrix_alloc(3, 3);
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result->tmp_mat_used = 0;
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result->tmp_vec = malloc(MAX_TEMP_MATRICES*sizeof(gsl_vector*));
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for(int i = 0; i < MAX_TEMP_MATRICES; i++)
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result->tmp_vec[i] = gsl_vector_alloc(3);
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result->tmp_vec_used = 0;
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return result;
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}
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void workspace_free(workspace_t *workspace)
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{
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gsl_eigen_nonsymmv_free(workspace->work_nonsymmv);
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gsl_eigen_symmv_free(workspace->work_symmv);
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gsl_vector_free(workspace->work_sv);
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gsl_vector_complex_free(workspace->eval_complex);
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gsl_matrix_complex_free(workspace->evec_complex);
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gsl_vector_free(workspace->eval_real);
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gsl_matrix_free(workspace->evec_real);
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gsl_permutation_free(workspace->permutation);
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for(int i = 0; i < MAX_TEMP_MATRICES; i++)
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gsl_matrix_free(workspace->tmp_mat[i]);
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free(workspace->tmp_mat);
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for(int i = 0; i < MAX_TEMP_VECTORS; i++)
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gsl_vector_free(workspace->tmp_vec[i]);
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free(workspace->tmp_vec);
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}
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/************************************************** basic operations ********************************************************/
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void invert(gsl_matrix *in, gsl_matrix *out, workspace_t *ws)
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{
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int s;
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gsl_matrix *tmp = getTempMatrix(ws);
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gsl_matrix_memcpy(tmp, in);
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gsl_linalg_LU_decomp(tmp, ws->permutation, &s);
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gsl_linalg_LU_invert(tmp, ws->permutation, out);
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releaseTempMatrices(ws, 1);
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}
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void solve(gsl_matrix *A, gsl_vector *b, gsl_vector *result, workspace_t *ws)
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{
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int s;
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gsl_matrix *tmp = getTempMatrix(ws);
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gsl_matrix_memcpy(tmp, A);
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gsl_linalg_LU_decomp(tmp, ws->permutation, &s);
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gsl_linalg_LU_solve(tmp, ws->permutation, b, result);
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releaseTempMatrices(ws, 1);
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}
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void conjugate(gsl_matrix *in, gsl_matrix *conjugator, gsl_matrix *out, workspace_t *ws)
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{
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gsl_matrix *tmp = getTempMatrix(ws);
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invert(conjugator, out, ws); // use out to temporarily store inverse conjugator
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gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, in, out, 0.0, tmp); // in * conjugator^{-1}
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gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, conjugator, tmp, 0.0, out);
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releaseTempMatrices(ws, 1);
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}
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void multiply(gsl_matrix *a, gsl_matrix *b, gsl_matrix *out)
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{
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gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, a, b, 0.0, out);
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}
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void multiply_right(gsl_matrix *a, gsl_matrix *b, workspace_t *ws)
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{
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gsl_matrix *tmp = getTempMatrix(ws);
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gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, a, b, 0.0, tmp);
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gsl_matrix_memcpy(a, tmp);
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releaseTempMatrices(ws, 1);
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}
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void multiply_left(gsl_matrix *a, gsl_matrix *b, workspace_t *ws)
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{
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gsl_matrix *tmp = getTempMatrix(ws);
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gsl_blas_dgemm(CblasNoTrans, CblasNoTrans, 1.0, a, b, 0.0, tmp);
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gsl_matrix_memcpy(b, tmp);
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releaseTempMatrices(ws, 1);
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}
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void multiply_many(workspace_t *ws, gsl_matrix *out, int n, ...)
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{
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va_list args;
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va_start(args, n);
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gsl_matrix_set_identity(out);
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for(int i = 0; i < n; i++) {
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gsl_matrix *cur = va_arg(args, gsl_matrix *);
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multiply_right(out, cur, ws);
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}
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va_end(args);
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}
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void cartan_calc(gsl_matrix *g, double *mu, workspace_t *ws)
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{
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gsl_matrix *tmp = getTempMatrix(ws);
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gsl_matrix_memcpy(tmp, g);
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gsl_linalg_SV_decomp(tmp, ws->evec_real, ws->eval_real, ws->work_sv);
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for(int i = 0; i < ws->n - 1; i++)
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mu[i] = log(gsl_vector_get(ws->eval_real, i) / gsl_vector_get(ws->eval_real, i+1));
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releaseTempMatrices(ws, 1);
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}
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void initialize(gsl_matrix *g, double *data, int x, int y)
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{
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gsl_matrix_view view = gsl_matrix_view_array(data, x, y);
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gsl_matrix_memcpy(g, &view.matrix);
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}
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void rotation_matrix(gsl_matrix *g, double *vector)
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{
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double normalized[3];
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double norm = sqrt(vector[0]*vector[0] + vector[1]*vector[1] + vector[2]*vector[2]);
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for(int i = 0; i < 3; i++)
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normalized[i] = vector[i] / norm;
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gsl_matrix_set_identity(g);
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gsl_matrix_set(g, 0, 0, cos(norm));
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gsl_matrix_set(g, 0, 1, -sin(norm) * normalized[2]);
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gsl_matrix_set(g, 0, 2, +sin(norm) * normalized[1]);
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gsl_matrix_set(g, 1, 0, +sin(norm) * normalized[2]);
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gsl_matrix_set(g, 1, 1, cos(norm));
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gsl_matrix_set(g, 1, 2, -sin(norm) * normalized[0]);
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gsl_matrix_set(g, 2, 0, -sin(norm) * normalized[1]);
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gsl_matrix_set(g, 2, 1, +sin(norm) * normalized[0]);
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gsl_matrix_set(g, 2, 2, cos(norm));
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for(int i = 0; i < 3; i++)
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for(int j = 0; j < 3; j++)
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g->data[i * g->tda + j] += (1 - cos(norm)) * normalized[i] * normalized[j];
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}
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double trace(gsl_matrix *g)
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{
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||||
return gsl_matrix_get(g, 0, 0) + gsl_matrix_get(g, 1, 1) + gsl_matrix_get(g, 2, 2);
|
||||
}
|
||||
|
||||
double determinant(gsl_matrix *g, workspace_t *ws)
|
||||
{
|
||||
int s;
|
||||
double result;
|
||||
gsl_matrix *tmp = getTempMatrix(ws);
|
||||
|
||||
gsl_matrix_memcpy(tmp, g);
|
||||
gsl_linalg_LU_decomp(tmp, ws->permutation, &s);
|
||||
result = gsl_linalg_LU_det(tmp, s);
|
||||
|
||||
releaseTempMatrices(ws, 1);
|
||||
return result;
|
||||
}
|
||||
|
||||
|
||||
int eigenvectors(gsl_matrix *g, gsl_matrix *evec_real, workspace_t *ws)
|
||||
{
|
||||
gsl_matrix *g_ = getTempMatrix(ws);
|
||||
int success = 0;
|
||||
|
||||
gsl_matrix_memcpy(g_, g);
|
||||
gsl_eigen_nonsymmv_params(0, ws->work_nonsymmv);
|
||||
int r = gsl_eigen_nonsymmv(g_, ws->eval_complex, ws->evec_complex, ws->work_nonsymmv);
|
||||
ERROR(r, "gsl_eigen_nonsymmv failed!\n");
|
||||
|
||||
gsl_eigen_nonsymmv_sort(ws->eval_complex, ws->evec_complex, GSL_EIGEN_SORT_ABS_DESC);
|
||||
|
||||
int real = 1;
|
||||
for(int i = 0; i < ws->n; i++)
|
||||
if(FCMP(GSL_IMAG(gsl_vector_complex_get(ws->eval_complex, i)), 0) != 0)
|
||||
real = 0;
|
||||
|
||||
if(!real)
|
||||
goto eigenvectors_out;
|
||||
|
||||
for(int i = 0; i < ws->n; i++)
|
||||
for(int j = 0; j < ws->n; j++)
|
||||
gsl_matrix_set(evec_real, i, j, GSL_REAL(gsl_matrix_complex_get(ws->evec_complex, i, j)));
|
||||
|
||||
success = 1;
|
||||
|
||||
eigenvectors_out:
|
||||
releaseTempMatrices(ws, 1);
|
||||
return success;
|
||||
}
|
||||
|
||||
// only fills in the real eigenvectors and returns their count
|
||||
int real_eigenvectors(gsl_matrix *g, gsl_matrix *evec_real, workspace_t *ws)
|
||||
{
|
||||
gsl_matrix *g_ = getTempMatrix(ws);
|
||||
|
||||
gsl_matrix_memcpy(g_, g);
|
||||
gsl_eigen_nonsymmv_params(0, ws->work_nonsymmv);
|
||||
int r = gsl_eigen_nonsymmv(g_, ws->eval_complex, ws->evec_complex, ws->work_nonsymmv);
|
||||
ERROR(r, "gsl_eigen_nonsymmv failed!\n");
|
||||
|
||||
gsl_eigen_nonsymmv_sort(ws->eval_complex, ws->evec_complex, GSL_EIGEN_SORT_ABS_DESC);
|
||||
|
||||
int real = 0;
|
||||
|
||||
for(int i = 0; i < ws->n; i++) {
|
||||
if(FCMP(GSL_IMAG(gsl_vector_complex_get(ws->eval_complex, i)), 0) == 0) {// real
|
||||
if(evec_real) {
|
||||
for(int j = 0; j < ws->n; j++)
|
||||
gsl_matrix_set(evec_real, j, real, GSL_REAL(gsl_matrix_complex_get(ws->evec_complex, j, i)));
|
||||
}
|
||||
real++;
|
||||
}
|
||||
}
|
||||
|
||||
releaseTempMatrices(ws, 1);
|
||||
return real;
|
||||
}
|
||||
|
||||
void eigensystem_symm(gsl_matrix *g, gsl_vector *eval, gsl_matrix *evec, workspace_t *ws)
|
||||
{
|
||||
gsl_matrix *g_ = getTempMatrix(ws);
|
||||
|
||||
gsl_matrix_memcpy(g_, g);
|
||||
int r = gsl_eigen_symmv (g_, eval, evec, ws->work_symmv);
|
||||
ERROR(r, "gsl_eigen_symmv failed!\n");
|
||||
|
||||
gsl_eigen_symmv_sort(eval, evec, GSL_EIGEN_SORT_ABS_DESC);
|
||||
|
||||
releaseTempMatrices(ws, 1);
|
||||
}
|
||||
|
||||
// returns number of positive directions and matrix transforming TO diagonal basis
|
||||
int diagonalize_symmetric_form(gsl_matrix *A, gsl_matrix *cob, workspace_t *ws)
|
||||
{
|
||||
gsl_matrix *A_ = getTempMatrix(ws);
|
||||
|
||||
gsl_matrix_memcpy(A_, A);
|
||||
int r = gsl_eigen_symmv (A_, ws->eval_real, cob, ws->work_symmv);
|
||||
ERROR(r, "gsl_eigen_symmv failed!\n");
|
||||
|
||||
gsl_eigen_symmv_sort(ws->eval_real, cob, GSL_EIGEN_SORT_VAL_ASC);
|
||||
|
||||
gsl_matrix_transpose(cob);
|
||||
|
||||
int positive = 0;
|
||||
|
||||
for(int i = 0; i < ws->n; i++) {
|
||||
if(gsl_vector_get(ws->eval_real, i) > 0)
|
||||
positive++;
|
||||
|
||||
for(int j = 0; j < ws->n; j++)
|
||||
*gsl_matrix_ptr(cob, i, j) *= sqrt(fabs(gsl_vector_get(ws->eval_real, i)));
|
||||
}
|
||||
|
||||
releaseTempMatrices(ws, 1);
|
||||
return positive;
|
||||
}
|
||||
|
||||
// computes a matrix in SL(3, R) which projectively transforms (e1, e2, e3, e1+e2+e3) to the 4 given vectors
|
||||
void projective_frame(gsl_vector **vertices, gsl_matrix *result, workspace_t *ws)
|
||||
{
|
||||
gsl_matrix *tmp = getTempMatrix(ws);
|
||||
gsl_vector *coeff = getTempVector(ws);
|
||||
int s;
|
||||
double det, scale;
|
||||
|
||||
for(int i = 0; i < 3; i++)
|
||||
for(int j = 0; j < 3; j++)
|
||||
gsl_matrix_set(tmp, i, j, gsl_vector_get(vertices[j], i));
|
||||
|
||||
gsl_linalg_LU_decomp(tmp, ws->permutation, &s);
|
||||
gsl_linalg_LU_solve(tmp, ws->permutation, vertices[3], coeff);
|
||||
det = gsl_linalg_LU_det(tmp, s);
|
||||
|
||||
for(int i = 0; i < 3; i++)
|
||||
det *= gsl_vector_get(coeff, i);
|
||||
scale = 1/cbrt(det);
|
||||
|
||||
for(int i = 0; i < 3; i++)
|
||||
for(int j = 0; j < 3; j++)
|
||||
gsl_matrix_set(result, i, j, scale*gsl_vector_get(vertices[j], i)*gsl_vector_get(coeff, j));
|
||||
|
||||
releaseTempMatrices(ws, 1);
|
||||
releaseTempVectors(ws, 1);
|
||||
}
|
||||
|
||||
void rotation_frame(gsl_matrix *rotation, gsl_matrix *result, workspace_t *ws)
|
||||
{
|
||||
gsl_matrix *tmp = getTempMatrix(ws);
|
||||
gsl_matrix *rot_basis = getTempMatrix(ws);
|
||||
|
||||
gsl_matrix_memcpy(tmp, rotation);
|
||||
gsl_eigen_nonsymmv_params(0, ws->work_nonsymmv);
|
||||
int r = gsl_eigen_nonsymmv(tmp, ws->eval_complex, ws->evec_complex, ws->work_nonsymmv);
|
||||
ERROR(r, "gsl_eigen_nonsymmv failed!\n");
|
||||
|
||||
double arg, minarg = 5; // greater than pi
|
||||
int minidx;
|
||||
for(int i = 0; i < 3; i++) {
|
||||
arg = gsl_complex_arg(gsl_vector_complex_get(ws->eval_complex, i));
|
||||
if(abs(arg) < minarg)
|
||||
{
|
||||
minidx = i;
|
||||
minarg = abs(arg);
|
||||
}
|
||||
}
|
||||
ERROR(FCMP(minarg, 0.0) != 0, "rotation_frame() failed! No eigenvalue was 1.\n");
|
||||
|
||||
for(int i = 0; i < 3; i++) {
|
||||
gsl_complex x = gsl_matrix_complex_get(ws->evec_complex, i, (minidx+1)%3);
|
||||
gsl_complex y = gsl_matrix_complex_get(ws->evec_complex, i, (minidx+2)%3);
|
||||
gsl_complex z = gsl_matrix_complex_get(ws->evec_complex, i, minidx);
|
||||
gsl_matrix_set(result, i, 0, GSL_REAL(x)+GSL_REAL(y));
|
||||
gsl_matrix_set(result, i, 1, GSL_IMAG(x)-GSL_IMAG(y));
|
||||
gsl_matrix_set(result, i, 2, GSL_REAL(z));
|
||||
}
|
||||
|
||||
releaseTempMatrices(ws, 2);
|
||||
}
|
||||
98
linalg.h
98
linalg.h
|
|
@ -1,98 +0,0 @@
|
|||
#ifndef LINALG_H
|
||||
#define LINALG_H
|
||||
|
||||
#include <stdio.h>
|
||||
#include <stdlib.h>
|
||||
#include <stdarg.h>
|
||||
#include <gsl/gsl_math.h>
|
||||
#include <gsl/gsl_eigen.h>
|
||||
#include <gsl/gsl_blas.h>
|
||||
#include <gsl/gsl_linalg.h>
|
||||
#include <memory.h>
|
||||
|
||||
#define ERROR(condition, msg, ...) if(condition){fprintf(stderr, msg, ##__VA_ARGS__); exit(1);}
|
||||
#define FCMP(x, y) gsl_fcmp(x, y, 1e-10)
|
||||
|
||||
#define MAX_TEMP_MATRICES 10
|
||||
#define MAX_TEMP_VECTORS 10
|
||||
|
||||
typedef struct _workspace {
|
||||
int n;
|
||||
gsl_eigen_nonsymmv_workspace *work_nonsymmv;
|
||||
gsl_eigen_symmv_workspace *work_symmv;
|
||||
gsl_vector *work_sv;
|
||||
gsl_vector_complex *eval_complex;
|
||||
gsl_matrix_complex *evec_complex;
|
||||
gsl_vector *eval_real;
|
||||
gsl_matrix *evec_real;
|
||||
gsl_permutation *permutation;
|
||||
|
||||
gsl_matrix **tmp_mat;
|
||||
int tmp_mat_used;
|
||||
gsl_vector **tmp_vec;
|
||||
int tmp_vec_used;
|
||||
} workspace_t;
|
||||
|
||||
workspace_t *workspace_alloc(int n);
|
||||
void workspace_free(workspace_t *workspace);
|
||||
void solve(gsl_matrix *A, gsl_vector *b, gsl_vector *result, workspace_t *ws);
|
||||
void invert(gsl_matrix *in, gsl_matrix *out, workspace_t *ws);
|
||||
void conjugate(gsl_matrix *in, gsl_matrix *conjugator, gsl_matrix *out, workspace_t *ws);
|
||||
void multiply(gsl_matrix *a, gsl_matrix *b, gsl_matrix *out);
|
||||
void multiply_right(gsl_matrix *a, gsl_matrix *b, workspace_t *ws);
|
||||
void multiply_left(gsl_matrix *a, gsl_matrix *b, workspace_t *ws);
|
||||
void multiply_many(workspace_t *ws, gsl_matrix *out, int n, ...);
|
||||
void cartan_calc(gsl_matrix *g, double *mu, workspace_t *ws);
|
||||
void initialize(gsl_matrix *g, double *data, int x, int y);
|
||||
void rotation_matrix(gsl_matrix *g, double *vector);
|
||||
int jordan_calc(gsl_matrix *g, double *mu, workspace_t *ws);
|
||||
double trace(gsl_matrix *g);
|
||||
double determinant(gsl_matrix *g, workspace_t *ws);
|
||||
int eigenvectors(gsl_matrix *g, gsl_matrix *evec, workspace_t *ws);
|
||||
int real_eigenvectors(gsl_matrix *g, gsl_matrix *evec, workspace_t *ws);
|
||||
void eigenvectors_symm(gsl_matrix *g, gsl_vector *eval, gsl_matrix *evec, workspace_t *ws);
|
||||
int diagonalize_symmetric_form(gsl_matrix *A, gsl_matrix *cob, workspace_t *ws);
|
||||
void projective_frame(gsl_vector **vertices, gsl_matrix *result, workspace_t *ws);
|
||||
void rotation_frame(gsl_matrix *rotation, gsl_matrix *result, workspace_t *ws);
|
||||
|
||||
// matrix allocation stuff
|
||||
|
||||
static gsl_matrix **getTempMatrices(workspace_t *ws, int n)
|
||||
{
|
||||
ERROR(ws->tmp_mat_used + n > MAX_TEMP_MATRICES, "Ran out of temporary matrices. Consider increasing MAX_TEMP_MATRICES\n");
|
||||
int index = ws->tmp_mat_used;
|
||||
ws->tmp_mat_used += n;
|
||||
return ws->tmp_mat + index;
|
||||
}
|
||||
|
||||
static gsl_matrix *getTempMatrix(workspace_t *ws)
|
||||
{
|
||||
return *getTempMatrices(ws, 1);
|
||||
}
|
||||
|
||||
static void releaseTempMatrices(workspace_t *ws, int n)
|
||||
{
|
||||
ERROR(ws->tmp_mat_used - n < 0, "Released more matrices then in use\n");
|
||||
ws->tmp_mat_used -= n;
|
||||
}
|
||||
|
||||
static gsl_vector **getTempVectors(workspace_t *ws, int n)
|
||||
{
|
||||
ERROR(ws->tmp_vec_used + n > MAX_TEMP_VECTORS, "Ran out of temporary vectors. Consider increasing MAX_TEMP_VECTORS\n");
|
||||
int index = ws->tmp_vec_used;
|
||||
ws->tmp_vec_used += n;
|
||||
return ws->tmp_vec + index;
|
||||
}
|
||||
|
||||
static gsl_vector *getTempVector(workspace_t *ws)
|
||||
{
|
||||
return *getTempVectors(ws, 1);
|
||||
}
|
||||
|
||||
static void releaseTempVectors(workspace_t *ws, int n)
|
||||
{
|
||||
ERROR(ws->tmp_vec_used - n < 0, "Released more vectors then in use\n");
|
||||
ws->tmp_vec_used -= n;
|
||||
}
|
||||
|
||||
#endif
|
||||
|
|
@ -1,18 +0,0 @@
|
|||
set log x
|
||||
set y2tics
|
||||
set xrange [exp(-1):1]
|
||||
set yrange [1.5:2]
|
||||
set y2range [1.98:2.1]
|
||||
set grid
|
||||
|
||||
# set terminal pngcairo enhanced size 1500,1000
|
||||
# set output "output/max_slope.png"
|
||||
|
||||
plot "output/max_slope_1621.dat" using 1:3 w lp pt 7 ps 0.6 lw 2 t "1621 elements", \
|
||||
"output/max_slope_24428.dat" using 1:3 w lp pt 7 ps 0.6 lw 2 t "24428 elements", \
|
||||
"output/max_slope_94252.dat" using 1:3 w lp lw 2 pt 7 ps 0.6 t "94252 elements", \
|
||||
"output/max_slope_713698.dat" using 1:3 w lp lw 2 pt 7 ps 0.6 t "713698 elements", \
|
||||
"output/max_slope_1621.dat" using 1:2 w p pt 7 ax x1y2 t "parameter"
|
||||
|
||||
pause mouse keypress
|
||||
if(MOUSE_KEY != 113) reread
|
||||
|
|
@ -1,32 +0,0 @@
|
|||
if(!exists("logt")) logt = log(1)
|
||||
if(!exists("logs")) logs = log(1)
|
||||
|
||||
#file = sprintf("< ./singular_values 713698 %f %f", exp(logs), exp(logt))
|
||||
file = sprintf("< ./singular_values 1621 %f %f", exp(logs), exp(logt))
|
||||
|
||||
set zeroaxis
|
||||
set samples 1000
|
||||
set size square
|
||||
set xrange [0:30]
|
||||
set yrange [0:30]
|
||||
set trange [0:5]
|
||||
set grid
|
||||
set parametric
|
||||
|
||||
plot file using 8:9 w p pt 7 ps 1 lc 1 t sprintf("t = %.2f", exp(logt))
|
||||
|
||||
#plot for[i=-10:10] log(tr(t,t*exp(log(2)*i/10.0))),log(trinv(t,t*exp(log(2)*i/10.0))) w l lw 2 t ""
|
||||
|
||||
#plot for[i=-10:10] t,log(tr(t,t*exp(log(2)*i/10.0)))-t w l lw 2 t ""
|
||||
|
||||
##plot for[i=20:20] t,log(tr(1/t,exp(2*log(2)*i/20.0-log(2)))) w l lw 2 t ""
|
||||
|
||||
#n=n+1
|
||||
#if(n < 1000) reread
|
||||
|
||||
pause mouse keypress
|
||||
if(MOUSE_KEY == 60) logt=logt-0.02
|
||||
if(MOUSE_KEY == 62) logt=logt+0.02
|
||||
if(MOUSE_KEY == 44) logs=logs-0.02
|
||||
if(MOUSE_KEY == 46) logs=logs+0.02
|
||||
if(MOUSE_KEY != 113) reread
|
||||
|
|
@ -1,23 +0,0 @@
|
|||
if(!exists("i")) i = 0
|
||||
|
||||
file = sprintf("< ./singular_values %f 1.78", exp((i-50)*0.02))
|
||||
|
||||
set samples 1000
|
||||
set size square
|
||||
set xrange [0:30]
|
||||
set yrange [0:30]
|
||||
set trange [0:30]
|
||||
set grid
|
||||
set parametric
|
||||
|
||||
set terminal pngcairo enhanced size 1024,1024
|
||||
img = sprintf("output/animation/test%03d.png", i);
|
||||
print sprintf("write %s", img)
|
||||
set output img
|
||||
|
||||
plot file using 6:7 w p pt 7 ps 0.5 lc 1 t columnheader, \
|
||||
t,2*t w l lw 2 t "", \
|
||||
t,t/2 w l lw 2 t ""
|
||||
|
||||
i=i+1
|
||||
if(i <= 100) reread
|
||||
|
|
@ -1,642 +0,0 @@
|
|||
#include "coxeter.h"
|
||||
//#include "linalg.h"
|
||||
#include "mat.h"
|
||||
|
||||
//#include <gsl/gsl_poly.h>
|
||||
#include <mps/mps.h>
|
||||
#include <mpi.h>
|
||||
#include <sys/stat.h>
|
||||
#include <sys/mman.h>
|
||||
#include <fcntl.h>
|
||||
#include <errno.h>
|
||||
#include <string.h>
|
||||
#include <unistd.h>
|
||||
|
||||
#define MIN(x,y) ((x)<(y)?(x):(y))
|
||||
#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
|
||||
#define DEBUG(msg, ...) do { print_time(); fprintf(stderr, msg, ##__VA_ARGS__); } while (0);
|
||||
//#define DEBUG(msg, ...)
|
||||
|
||||
#define TDIV 10
|
||||
#define TFROM 1
|
||||
#define TTO 9
|
||||
#define MDIV 10
|
||||
#define MFROM 1
|
||||
#define MTO 9
|
||||
#define JOBNR(t,m) (((t)-TFROM) + ((m)-MFROM)*(TTO-TFROM+1))
|
||||
#define NJOBS ((TTO-TFROM+1)*(MTO-MFROM+1))
|
||||
#define FLUSH_INTERVAL 100
|
||||
|
||||
enum message_tag {
|
||||
JOB_ORDER,
|
||||
JOB_RESULT,
|
||||
JOB_SHUTDOWN,
|
||||
};
|
||||
|
||||
struct job {
|
||||
int tparam, mparam;
|
||||
int done;
|
||||
double max_slope;
|
||||
double time;
|
||||
};
|
||||
|
||||
struct result {
|
||||
mpq_t tr;
|
||||
mpq_t trinv;
|
||||
};
|
||||
|
||||
struct global_data {
|
||||
int n;
|
||||
group_t *group;
|
||||
mat* matrices;
|
||||
struct result *invariants;
|
||||
struct result **distinct_invariants;
|
||||
mps_context *solver;
|
||||
};
|
||||
|
||||
|
||||
struct timespec starttime;
|
||||
char processor_name[MPI_MAX_PROCESSOR_NAME];
|
||||
int world_rank;
|
||||
int world_size;
|
||||
MPI_Datatype job_datatype;
|
||||
|
||||
void print_time()
|
||||
{
|
||||
double diff;
|
||||
struct timespec current;
|
||||
|
||||
clock_gettime(CLOCK_REALTIME, ¤t);
|
||||
|
||||
diff = (current.tv_sec - starttime.tv_sec) + (current.tv_nsec - starttime.tv_nsec)*1e-9;
|
||||
|
||||
fprintf(stderr, "[%04d %.3f] ", world_rank, diff);
|
||||
}
|
||||
|
||||
static struct global_data allocate_global_data(int n)
|
||||
{
|
||||
struct global_data result;
|
||||
result.n = n;
|
||||
result.matrices = malloc(n*sizeof(mat));
|
||||
for(int i = 0; i < n; i++)
|
||||
mat_init(result.matrices[i], 3);
|
||||
result.invariants = malloc(n*sizeof(struct result));
|
||||
result.distinct_invariants = malloc(n*sizeof(struct result*));
|
||||
for(int i = 0; i < n; i++) {
|
||||
mpq_init(result.invariants[i].tr);
|
||||
mpq_init(result.invariants[i].trinv);
|
||||
result.distinct_invariants[i] = &result.invariants[i];
|
||||
}
|
||||
result.solver = mps_context_new();
|
||||
mps_context_set_output_prec(result.solver, 20); // relative precision
|
||||
mps_context_set_output_goal(result.solver, MPS_OUTPUT_GOAL_APPROXIMATE);
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
void free_global_data(struct global_data dat)
|
||||
{
|
||||
for(int i = 0; i < dat.n; i++)
|
||||
mat_clear(dat.matrices[i]);
|
||||
free(dat.matrices);
|
||||
for(int i = 0; i < dat.n; i++) {
|
||||
mpq_clear(dat.invariants[i].tr);
|
||||
mpq_clear(dat.invariants[i].trinv);
|
||||
}
|
||||
free(dat.invariants);
|
||||
free(dat.distinct_invariants);
|
||||
mps_context_free(dat.solver);
|
||||
}
|
||||
|
||||
static int compare_result(const void *a_, const void *b_)
|
||||
{
|
||||
int d = 0;
|
||||
|
||||
struct result **a = (struct result **)a_;
|
||||
struct result **b = (struct result **)b_;
|
||||
|
||||
d = mpq_cmp((*a)->tr,(*b)->tr);
|
||||
if(d == 0)
|
||||
d = mpq_cmp((*a)->trinv, (*b)->trinv);
|
||||
|
||||
return d;
|
||||
}
|
||||
|
||||
int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues)
|
||||
{
|
||||
mpq_t coeff1, coeff2, zero;
|
||||
cplx_t *roots;
|
||||
double radii[3];
|
||||
double *radii_p[3];
|
||||
mps_monomial_poly *poly;
|
||||
mps_boolean errors;
|
||||
int result = 0;
|
||||
|
||||
mpq_inits(coeff1, coeff2, zero, NULL);
|
||||
mpq_set(coeff1, trinv);
|
||||
mpq_sub(coeff2, zero, tr);
|
||||
|
||||
poly = mps_monomial_poly_new(solv, 3);
|
||||
mps_monomial_poly_set_coefficient_int(solv, poly, 0, -1, 0);
|
||||
mps_monomial_poly_set_coefficient_q(solv, poly, 1, coeff1, zero);
|
||||
mps_monomial_poly_set_coefficient_q(solv, poly, 2, coeff2, zero);
|
||||
mps_monomial_poly_set_coefficient_int(solv, poly, 3, 1, 0);
|
||||
|
||||
mps_context_set_input_poly(solv, (mps_polynomial*)poly);
|
||||
mps_mpsolve(solv);
|
||||
|
||||
roots = cplx_valloc(3);
|
||||
for(int i = 0; i < 3; i++)
|
||||
radii_p[i] = &(radii[i]);
|
||||
mps_context_get_roots_d(solv, &roots, radii_p);
|
||||
errors = mps_context_has_errors(solv);
|
||||
|
||||
if(errors) {
|
||||
result = 1;
|
||||
} else {
|
||||
for(int i = 0; i < 3; i++) {
|
||||
eigenvalues[i] = cplx_Re(roots[i]);
|
||||
if(fabs(cplx_Im(roots[i])) > radii[i]) // non-real root
|
||||
result = 2;
|
||||
}
|
||||
}
|
||||
|
||||
cplx_vfree(roots);
|
||||
mpq_clears(coeff1, coeff2, zero, NULL);
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
void continued_fraction_approximation(mpq_t out, double in, int level)
|
||||
{
|
||||
mpq_t tmp;
|
||||
|
||||
if(in < 0) {
|
||||
mpq_init(tmp);
|
||||
mpq_set_ui(tmp, 0, 1);
|
||||
continued_fraction_approximation(out, -in, level);
|
||||
mpq_sub(out, tmp, out);
|
||||
mpq_clear(tmp);
|
||||
return;
|
||||
}
|
||||
|
||||
if(level == 0) {
|
||||
mpq_set_si(out, (signed long int)round(in), 1); // floor(in)
|
||||
} else {
|
||||
continued_fraction_approximation(out, 1/(in - floor(in)), level - 1);
|
||||
mpq_init(tmp);
|
||||
mpq_set_ui(tmp, 1, 1);
|
||||
mpq_div(out, tmp, out); // out -> 1/out
|
||||
mpq_set_si(tmp, (signed long int)in, 1); // floor(in)
|
||||
mpq_add(out, out, tmp);
|
||||
mpq_clear(tmp);
|
||||
}
|
||||
}
|
||||
|
||||
void quartic(mpq_t out, mpq_t in, int a, int b, int c, int d, int e)
|
||||
{
|
||||
mpq_t tmp;
|
||||
mpq_init(tmp);
|
||||
|
||||
mpq_set_si(out, a, 1);
|
||||
mpq_mul(out, out, in);
|
||||
mpq_set_si(tmp, b, 1);
|
||||
mpq_add(out, out, tmp);
|
||||
mpq_mul(out, out, in);
|
||||
mpq_set_si(tmp, c, 1);
|
||||
mpq_add(out, out, tmp);
|
||||
mpq_mul(out, out, in);
|
||||
mpq_set_si(tmp, d, 1);
|
||||
mpq_add(out, out, tmp);
|
||||
mpq_mul(out, out, in);
|
||||
mpq_set_si(tmp, e, 1);
|
||||
mpq_add(out, out, tmp);
|
||||
|
||||
mpq_clear(tmp);
|
||||
}
|
||||
|
||||
// this version is only for the (4,4,4) group
|
||||
void initialize_triangle_generators(mat_workspace *ws, mat *gen, mpq_t m, mpq_t t)
|
||||
{
|
||||
mpq_t s,sinv,q,x,y;
|
||||
mpq_t zero, one, two;
|
||||
mpq_t tmp;
|
||||
|
||||
mpq_inits(s,sinv,q,x,y,zero,one,two,tmp,NULL);
|
||||
mpq_set_ui(zero, 0, 1);
|
||||
mpq_set_ui(one, 1, 1);
|
||||
mpq_set_ui(two, 2, 1);
|
||||
|
||||
// s = (1-m^2)/2m
|
||||
mpq_mul(s, m, m);
|
||||
mpq_sub(s, one, s);
|
||||
mpq_div(s, s, m);
|
||||
mpq_div(s, s, two);
|
||||
mpq_div(sinv, one, s);
|
||||
|
||||
// q = (1+m^2)/(1-m^2) = 2/(1-m^2) - 1
|
||||
mpq_mul(q, m, m);
|
||||
mpq_sub(q, one, q);
|
||||
mpq_div(q, two, q);
|
||||
mpq_sub(q, q, one);
|
||||
|
||||
// x = -tq, y = -q/t
|
||||
mpq_mul(x, q, t);
|
||||
mpq_sub(x, zero, x);
|
||||
mpq_div(y, q, t);
|
||||
mpq_sub(y, zero, y);
|
||||
|
||||
// q^2 = xy = 1 + 1/s^2
|
||||
// [ -s s*y 0]
|
||||
// [ -s*x s*x*y - 1/s 0]
|
||||
// [ -s*y s*y^2 - x 1]
|
||||
LOOP(i,3) {
|
||||
mat_zero(gen[i]);
|
||||
mpq_sub(tmp, zero, s);
|
||||
mat_set(gen[i%3], i%3, i%3, tmp);
|
||||
mpq_mul(tmp, s, y);
|
||||
mat_set(gen[i%3], i%3, (i+1)%3, tmp);
|
||||
mpq_mul(tmp, s, x);
|
||||
mpq_sub(tmp, zero, tmp);
|
||||
mat_set(gen[i%3], (i+1)%3, i%3, tmp);
|
||||
mpq_mul(tmp, s, x);
|
||||
mpq_mul(tmp, tmp, y);
|
||||
mpq_sub(tmp, tmp, sinv);
|
||||
mat_set(gen[i%3], (i+1)%3, (i+1)%3, tmp);
|
||||
mpq_mul(tmp, s, y);
|
||||
mpq_sub(tmp, zero, tmp);
|
||||
mat_set(gen[i%3], (i+2)%3, i%3, tmp);
|
||||
mpq_mul(tmp, s, y);
|
||||
mpq_mul(tmp, tmp, y);
|
||||
mpq_sub(tmp, tmp, x);
|
||||
mat_set(gen[i%3], (i+2)%3, (i+1)%3, tmp);
|
||||
mat_set(gen[i%3], (i+2)%3, (i+2)%3, one);
|
||||
}
|
||||
|
||||
LOOP(i,3) mat_pseudoinverse(ws, gen[i+3], gen[i]);
|
||||
|
||||
// debug output
|
||||
/*
|
||||
gmp_printf("m = %Qd, s = %Qd, t = %Qd, q = %Qd, x = %Qd, y = %Qd\n", m, s, t, q, x, y);
|
||||
mat_print(gen[0]);
|
||||
mat_print(gen[1]);
|
||||
mat_print(gen[2]);
|
||||
*/
|
||||
|
||||
mpq_inits(s,sinv,q,x,y,zero,one,two,tmp,NULL);
|
||||
}
|
||||
|
||||
char *print_word(groupelement_t *g, char *str)
|
||||
{
|
||||
int i = g->length - 1;
|
||||
|
||||
str[g->length] = 0;
|
||||
while(g->parent) {
|
||||
str[i--] = 'a' + g->letter;
|
||||
g = g->parent;
|
||||
}
|
||||
|
||||
return str;
|
||||
}
|
||||
|
||||
void enumerate(group_t *group, mat *matrices, mpq_t m, mpq_t t)
|
||||
{
|
||||
mat_workspace *ws;
|
||||
mat tmp;
|
||||
mat gen[6];
|
||||
char buf[100], buf2[100], buf3[100];
|
||||
|
||||
// allocate stuff
|
||||
ws = mat_workspace_init(3);
|
||||
for(int i = 0; i < 6; i++)
|
||||
mat_init(gen[i], 3);
|
||||
mat_init(tmp, 3);
|
||||
|
||||
initialize_triangle_generators(ws, gen, m, t);
|
||||
|
||||
mat_identity(matrices[0]);
|
||||
for(int i = 1; i < group->size; i++) {
|
||||
if(group->elements[i].length % 2 != 0)
|
||||
continue;
|
||||
if(!group->elements[i].inverse)
|
||||
continue;
|
||||
|
||||
int parent = group->elements[i].parent->id;
|
||||
int grandparent = group->elements[i].parent->parent->id;
|
||||
int letter;
|
||||
|
||||
if(group->elements[parent].letter == 1 && group->elements[i].letter == 2)
|
||||
letter = 0; // p = bc
|
||||
else if(group->elements[parent].letter == 2 && group->elements[i].letter == 0)
|
||||
letter = 1; // q = ca
|
||||
else if(group->elements[parent].letter == 0 && group->elements[i].letter == 1)
|
||||
letter = 2; // r = ab
|
||||
if(group->elements[parent].letter == 2 && group->elements[i].letter == 1)
|
||||
letter = 3; // p^{-1} = cb
|
||||
else if(group->elements[parent].letter == 0 && group->elements[i].letter == 2)
|
||||
letter = 4; // q^{-1} = ac
|
||||
else if(group->elements[parent].letter == 1 && group->elements[i].letter == 0)
|
||||
letter = 5; // r^{-1} = ba
|
||||
|
||||
mat_multiply(ws, matrices[i], matrices[grandparent], gen[letter]);
|
||||
}
|
||||
|
||||
// free stuff
|
||||
for(int i = 0; i < 6; i++)
|
||||
mat_clear(gen[i]);
|
||||
mat_clear(tmp);
|
||||
mat_workspace_clear(ws);
|
||||
}
|
||||
|
||||
|
||||
double compute_max_slope(struct global_data dat, mpq_t t, mpq_t m)
|
||||
{
|
||||
// mpq_set_ui(t, ttick, 100);
|
||||
// mpq_set_ui(m, mtick, 100); // 414/1000 ~ sqrt(2)-1 <-> s=1
|
||||
// s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m));
|
||||
|
||||
int n = 0;
|
||||
int nmax = dat.n;
|
||||
int nuniq;
|
||||
double max_slope;
|
||||
int retval;
|
||||
double evs[3];
|
||||
|
||||
group_t *group = dat.group;
|
||||
mat *matrices = dat.matrices;
|
||||
struct result *invariants = dat.invariants;
|
||||
struct result **distinct_invariants = dat.distinct_invariants;
|
||||
mps_context *solver = dat.solver;
|
||||
|
||||
// DEBUG("Compute matrices\n");
|
||||
enumerate(group, matrices, m, t);
|
||||
|
||||
// DEBUG("Compute traces\n");
|
||||
n = 0;
|
||||
for(int i = 0; i < nmax; i++) {
|
||||
if(group->elements[i].length % 2 != 0 || !group->elements[i].inverse)
|
||||
continue;
|
||||
|
||||
mat_trace(invariants[i].tr, matrices[i]);
|
||||
mat_trace(invariants[i].trinv, matrices[group->elements[i].inverse->id]);
|
||||
|
||||
distinct_invariants[n++] = &invariants[i];
|
||||
}
|
||||
|
||||
// DEBUG("Get unique traces\n");
|
||||
|
||||
qsort(distinct_invariants, n, sizeof(struct result*), compare_result);
|
||||
|
||||
nuniq = 0;
|
||||
for(int i = 0; i < n; i++) {
|
||||
if(i == 0 || compare_result(&distinct_invariants[i], &distinct_invariants[nuniq-1]) != 0)
|
||||
distinct_invariants[nuniq++] = distinct_invariants[i];
|
||||
}
|
||||
|
||||
max_slope = 0;
|
||||
int max_slope_index;
|
||||
|
||||
// DEBUG("Solve characteristic polynomials\n");
|
||||
for(int i = 0; i < nuniq; i++) {
|
||||
retval = solve_characteristic_polynomial(solver, distinct_invariants[i]->tr, distinct_invariants[i]->trinv, evs);
|
||||
if(retval == 1) {
|
||||
fprintf(stderr, "Error! Could not solve polynomial.\n");
|
||||
continue;
|
||||
} else if(retval == 2) {
|
||||
continue;
|
||||
}
|
||||
|
||||
if(fabs(evs[0]) < fabs(evs[1]))
|
||||
SWAP(double, evs[0], evs[1]);
|
||||
if(fabs(evs[1]) < fabs(evs[2]))
|
||||
SWAP(double, evs[1], evs[2]);
|
||||
if(fabs(evs[0]) < fabs(evs[1]))
|
||||
SWAP(double, evs[0], evs[1]);
|
||||
|
||||
double x = log(fabs(evs[0]));
|
||||
double y = -log(fabs(evs[2]));
|
||||
|
||||
if(y/x > max_slope && (x > 0.1 || y > 0.1)) {
|
||||
max_slope_index = distinct_invariants[i] - invariants;
|
||||
max_slope = y/x;
|
||||
}
|
||||
|
||||
// gmp_printf("%Qd %Qd %f %f %f\n", distinct_invariants[i]->tr, distinct_invariants[i]->trinv, x, y, y/x);
|
||||
}
|
||||
|
||||
return max_slope;
|
||||
}
|
||||
|
||||
void write_results_and_end(struct job *jobs, const char *outfile)
|
||||
{
|
||||
DEBUG("writing output and shutting down\n");
|
||||
|
||||
FILE *f = fopen(outfile, "w");
|
||||
for(int i = 0; i < NJOBS; i++)
|
||||
fprintf(f, "%d/%d %d/%d %.10f %.10f %.10f %.3f\n",
|
||||
jobs[i].tparam, TDIV, jobs[i].mparam, MDIV,
|
||||
(double)jobs[i].tparam/TDIV, (double)jobs[i].mparam/MDIV, jobs[i].max_slope,
|
||||
jobs[i].time);
|
||||
fclose(f);
|
||||
|
||||
for(int i = 1; i < world_size; i++)
|
||||
MPI_Send(NULL, 0, job_datatype, i, JOB_SHUTDOWN, MPI_COMM_WORLD);
|
||||
|
||||
}
|
||||
|
||||
void run_master_process(int nmax, const char *restart, const char *outfile)
|
||||
{
|
||||
int total_jobs = NJOBS;
|
||||
int completed = 0;
|
||||
int queue_jobs = MIN(total_jobs, 2*world_size);
|
||||
struct job current_job;
|
||||
MPI_Status status;
|
||||
FILE *f;
|
||||
int continuing = 1;
|
||||
int restartf;
|
||||
struct job *alljobs;
|
||||
struct job *current;
|
||||
|
||||
restartf = open(restart, O_RDWR);
|
||||
if(restartf == -1 && errno == ENOENT) {
|
||||
restartf = open(restart, O_RDWR | O_CREAT, 0666);
|
||||
continuing = 0;
|
||||
}
|
||||
if(restartf == -1) {
|
||||
DEBUG("error opening restart file: %s\n", strerror(errno));
|
||||
exit(1);
|
||||
}
|
||||
ftruncate(restartf, total_jobs*sizeof(struct job));
|
||||
alljobs = (struct job*) mmap(0, total_jobs*sizeof(struct job), PROT_READ | PROT_WRITE, MAP_SHARED, restartf, 0);
|
||||
if(alljobs == MAP_FAILED) {
|
||||
DEBUG("error mapping restart file: %s\n", strerror(errno));
|
||||
exit(1);
|
||||
}
|
||||
|
||||
if(continuing) {
|
||||
for(int i = 0; i < total_jobs; i++)
|
||||
if(alljobs[i].done)
|
||||
completed++;
|
||||
} else {
|
||||
for(int tparam = TFROM; tparam <= TTO; tparam++) {
|
||||
for(int mparam = MFROM; mparam <= MTO; mparam++) {
|
||||
alljobs[JOBNR(tparam,mparam)].tparam = tparam;
|
||||
alljobs[JOBNR(tparam,mparam)].mparam = mparam;
|
||||
alljobs[JOBNR(tparam,mparam)].done = 0;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fsync(restartf);
|
||||
|
||||
if(continuing) {
|
||||
DEBUG("continuing from restart file, %d/%d jobs completed, %d nodes\n", completed, total_jobs, world_size);
|
||||
} else {
|
||||
DEBUG("starting from scratch, %d jobs, %d nodes\n", total_jobs, world_size);
|
||||
}
|
||||
|
||||
if(completed >= total_jobs)
|
||||
{
|
||||
write_results_and_end(alljobs, outfile);
|
||||
goto cleanup;
|
||||
}
|
||||
|
||||
// assign initial jobs
|
||||
current = alljobs-1;
|
||||
for(int i = 0; i < 2*world_size; i++) {
|
||||
do {
|
||||
current++;
|
||||
} while(current < alljobs + total_jobs && current->done);
|
||||
if(current >= alljobs + total_jobs) // all jobs are assigned
|
||||
break;
|
||||
MPI_Send(current, 1, job_datatype, 1 + i%(world_size-1), JOB_ORDER, MPI_COMM_WORLD);
|
||||
}
|
||||
|
||||
while(1) {
|
||||
MPI_Probe(MPI_ANY_SOURCE, MPI_ANY_TAG, MPI_COMM_WORLD, &status);
|
||||
if(status.MPI_TAG == JOB_RESULT) {
|
||||
MPI_Recv(¤t_job, 1, job_datatype, MPI_ANY_SOURCE, JOB_RESULT, MPI_COMM_WORLD, &status);
|
||||
completed++;
|
||||
|
||||
DEBUG("job (%d,%d) completed by instance %d in %f seconds, result = %.3f, %d/%d done\n",
|
||||
current_job.tparam, current_job.mparam,
|
||||
status.MPI_SOURCE, current_job.time, current_job.max_slope, completed, total_jobs);
|
||||
|
||||
int nr = JOBNR(current_job.tparam, current_job.mparam);
|
||||
memcpy(&alljobs[nr], ¤t_job, sizeof(struct job));
|
||||
alljobs[nr].done = 1;
|
||||
|
||||
if(completed % FLUSH_INTERVAL == 0)
|
||||
fsync(restartf);
|
||||
|
||||
// find the next unassigned job
|
||||
do {
|
||||
current++;
|
||||
} while(current < alljobs + total_jobs && current->done);
|
||||
|
||||
if(current < alljobs + total_jobs) {
|
||||
MPI_Send(current, 1, job_datatype, status.MPI_SOURCE, JOB_ORDER, MPI_COMM_WORLD);
|
||||
}
|
||||
|
||||
if(completed >= total_jobs) {
|
||||
write_results_and_end(alljobs, outfile);
|
||||
goto cleanup;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
cleanup:
|
||||
|
||||
munmap(alljobs, total_jobs*sizeof(struct job));
|
||||
close(restartf);
|
||||
}
|
||||
|
||||
int main(int argc, char *argv[])
|
||||
{
|
||||
int name_len;
|
||||
|
||||
MPI_Status status;
|
||||
|
||||
mpq_t m, t;
|
||||
double s;
|
||||
struct job current_job;
|
||||
int nmax;
|
||||
double max_slope;
|
||||
struct global_data dat;
|
||||
double jobtime;
|
||||
|
||||
clock_gettime(CLOCK_REALTIME, &starttime);
|
||||
|
||||
if(argc < 4) {
|
||||
fprintf(stderr, "Usage: mpirun -n <nr> --hostfile <hostfile> %s <number of elements> <restartfile> <outfile>\n", argv[0]);
|
||||
return 0;
|
||||
}
|
||||
nmax = atoi(argv[1]);
|
||||
|
||||
MPI_Init(NULL, NULL);
|
||||
MPI_Comm_size(MPI_COMM_WORLD, &world_size);
|
||||
MPI_Comm_rank(MPI_COMM_WORLD, &world_rank);
|
||||
MPI_Get_processor_name(processor_name, &name_len);
|
||||
|
||||
// DEBUG("instance %d/%d started on %s\n", world_rank, world_size, processor_name);
|
||||
|
||||
int blocklengths[2] = {3, 2};
|
||||
MPI_Datatype types[2] = {MPI_INT, MPI_DOUBLE};
|
||||
MPI_Aint displacements[2] = {(size_t)&((struct job*)0)->tparam, (size_t)&((struct job*)0)->max_slope};
|
||||
MPI_Type_create_struct(2, blocklengths, displacements, types, &job_datatype);
|
||||
MPI_Type_commit(&job_datatype);
|
||||
|
||||
if(world_rank == 0) { // master processor
|
||||
run_master_process(nmax, argv[2], argv[3]);
|
||||
MPI_Finalize();
|
||||
return 0;
|
||||
}
|
||||
|
||||
// DEBUG("Allocate & generate group\n");
|
||||
mpq_inits(m, t, NULL);
|
||||
dat = allocate_global_data(nmax);
|
||||
dat.group = coxeter_init_triangle(4, 4, 4, nmax);
|
||||
|
||||
// fprintf(stderr, "max word length = %d\n", dat.group->elements[nmax-1].length);
|
||||
|
||||
while(1) {
|
||||
MPI_Probe(0, MPI_ANY_TAG, MPI_COMM_WORLD, &status);
|
||||
// MPI_Recv(¤t_job, 1, job_datatype, 0, MPI_ANY_TAG, MPI_COMM_WORLD, &status);
|
||||
if(status.MPI_TAG == JOB_SHUTDOWN) {
|
||||
// DEBUG("instance %d shutting down\n", world_rank);
|
||||
break;
|
||||
}
|
||||
else if(status.MPI_TAG == JOB_ORDER) {
|
||||
MPI_Recv(¤t_job, 1, job_datatype, 0, MPI_ANY_TAG, MPI_COMM_WORLD, &status);
|
||||
DEBUG("instance %d starting order (%d,%d)\n", world_rank, current_job.tparam, current_job.mparam);
|
||||
|
||||
jobtime = -MPI_Wtime();
|
||||
|
||||
// do the actual work
|
||||
mpq_set_ui(t, current_job.tparam, TDIV);
|
||||
mpq_set_ui(m, current_job.mparam, MDIV);
|
||||
s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m));
|
||||
|
||||
max_slope = compute_max_slope(dat, t, m);
|
||||
|
||||
jobtime += MPI_Wtime();
|
||||
|
||||
// fprintf(stdout, "%.5f %.5f %.5f %f\n",
|
||||
// mpq_get_d(t), mpq_get_d(m), s, max_slope);
|
||||
current_job.max_slope = max_slope;
|
||||
current_job.time = jobtime;
|
||||
|
||||
DEBUG("instance %d finished order (%d,%d) in %f seconds\n", world_rank, current_job.tparam, current_job.mparam, jobtime);
|
||||
|
||||
MPI_Send(¤t_job, 1, job_datatype, 0, JOB_RESULT, MPI_COMM_WORLD);
|
||||
}
|
||||
}
|
||||
|
||||
// DEBUG("Clean up\n");
|
||||
coxeter_clear(dat.group);
|
||||
free_global_data(dat);
|
||||
mpq_clears(m, t, NULL);
|
||||
|
||||
MPI_Type_free(&job_datatype);
|
||||
MPI_Finalize();
|
||||
}
|
||||
|
|
@ -1,173 +0,0 @@
|
|||
#include "coxeter.h"
|
||||
#include "linalg.h"
|
||||
#include "mat.h"
|
||||
#include "enumerate_triangle_group.h"
|
||||
|
||||
#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
|
||||
#define DEBUG(msg, ...)
|
||||
|
||||
double mpq_log(mpq_t m_op)
|
||||
{
|
||||
static double logB = log(ULONG_MAX);
|
||||
|
||||
// Undefined logs (should probably return NAN in second case?)
|
||||
if (mpz_get_ui(mpq_numref(m_op)) == 0 || mpz_sgn(mpq_numref(m_op)) < 0)
|
||||
return -INFINITY;
|
||||
|
||||
// Log of numerator
|
||||
double lognum = log(mpq_numref(m_op)->_mp_d[abs(mpq_numref(m_op)->_mp_size) - 1]);
|
||||
lognum += (abs(mpq_numref(m_op)->_mp_size)-1) * logB;
|
||||
|
||||
// Subtract log of denominator, if it exists
|
||||
if (abs(mpq_denref(m_op)->_mp_size) > 0)
|
||||
{
|
||||
lognum -= log(mpq_denref(m_op)->_mp_d[abs(mpq_denref(m_op)->_mp_size)-1]);
|
||||
lognum -= (abs(mpq_denref(m_op)->_mp_size)-1) * logB;
|
||||
}
|
||||
return lognum;
|
||||
}
|
||||
|
||||
int main(int argc, char *argv[])
|
||||
{
|
||||
mpq_t m, t, s, q, tmp, tmp2;
|
||||
mat_workspace *ws;
|
||||
mat gen[6];
|
||||
mps_context *solver;
|
||||
mps_monomial_poly *poly;
|
||||
mat element, inverse;
|
||||
int letter1, letter2, letter;
|
||||
mpq_t tr, trinv;
|
||||
double x, y, slope;
|
||||
int retval;
|
||||
double evs[3];
|
||||
char buf[100];
|
||||
double max_slope = 0;
|
||||
int max_slope_index = 0;
|
||||
double min_slope = INFINITY;
|
||||
int min_slope_index = 0;
|
||||
char *env;
|
||||
int mode;
|
||||
|
||||
if(argc < 2) {
|
||||
fprintf(stderr,
|
||||
"Usage: %s <s> <q> <word1> <word2> ...\n"
|
||||
"Computes jordan slopes of a list of group elements for a fixed representation.\n"
|
||||
"s,q: representation in the Hitchin component, given as rational numbers, e.g. 2/7\n"
|
||||
"word1, word2, ...: elements in the triangle rotation group, given as reflection group words\n"
|
||||
"output: word - jordan slope pairs\n"
|
||||
"+max slope index, max slope value, max slope word, min slope index, min slope value, min slope word\n"
|
||||
"controlled by environment variable MAXIMUM=no/yes/only, default yes\n",
|
||||
argv[0]);
|
||||
exit(0);
|
||||
}
|
||||
|
||||
mpq_inits(m, t, s, q, tmp, tmp2, tr, trinv, NULL);
|
||||
ws = mat_workspace_init(3);
|
||||
for(int i = 0; i < 6; i++)
|
||||
mat_init(gen[i], 3);
|
||||
mat_init(element, 3);
|
||||
mat_init(inverse, 3);
|
||||
|
||||
solver = mps_context_new();
|
||||
poly = mps_monomial_poly_new(solver, 3);
|
||||
mps_context_set_output_prec(solver, 20); // relative precision
|
||||
mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
|
||||
|
||||
mpq_set_str(s, argv[1], 10);
|
||||
mpq_set_str(q, argv[2], 10);
|
||||
|
||||
env = getenv("MAXIMUM");
|
||||
if(!env || strcmp(env, "yes") == 0) {
|
||||
mode = 1; // yes
|
||||
} else if(strcmp(env, "no") == 0) {
|
||||
mode = 0; // no
|
||||
} else if(strcmp(env, "only") == 0) {
|
||||
mode = 2; // only
|
||||
}
|
||||
|
||||
for(int w = 0; w < argc - 3; w++) {
|
||||
initialize_triangle_generators(ws, gen, 6, 4, 3, s, q);
|
||||
|
||||
mat_identity(element);
|
||||
mat_identity(inverse);
|
||||
for(int k = 0; k < strlen(argv[w+3]); k+=2) {
|
||||
letter1 = argv[w+3][k] - 'a';
|
||||
letter2 = argv[w+3][k+1] - 'a';
|
||||
|
||||
if(letter1 == 1 && letter2 == 2)
|
||||
letter = 0; // p = bc
|
||||
else if(letter1 == 2 && letter2 == 0)
|
||||
letter = 1; // q = ca
|
||||
else if(letter1 == 0 && letter2 == 1)
|
||||
letter = 2; // r = ab
|
||||
else if(letter1 == 2 && letter2 == 1)
|
||||
letter = 3; // p^{-1} = cb
|
||||
else if(letter1 == 0 && letter2 == 2)
|
||||
letter = 4; // q^{-1} = ac
|
||||
else if(letter1 == 1 && letter2 == 0)
|
||||
letter = 5; // r^{-1} = ba
|
||||
|
||||
mat_multiply(ws, element, element, gen[letter]);
|
||||
mat_multiply(ws, inverse, gen[(letter+3)%6], inverse);
|
||||
}
|
||||
|
||||
mat_trace(tr, element);
|
||||
mat_trace(trinv, inverse);
|
||||
|
||||
retval = solve_characteristic_polynomial(solver, poly, tr, trinv, evs);
|
||||
if(retval == 1) {
|
||||
fprintf(stderr, "Error! Could not solve polynomial.\n");
|
||||
return 1;
|
||||
}
|
||||
|
||||
if(fabs(evs[0]) < fabs(evs[1]))
|
||||
SWAP(double, evs[0], evs[1]);
|
||||
if(fabs(evs[1]) < fabs(evs[2]))
|
||||
SWAP(double, evs[1], evs[2]);
|
||||
if(fabs(evs[0]) < fabs(evs[1]))
|
||||
SWAP(double, evs[0], evs[1]);
|
||||
|
||||
x = log(fabs(evs[0]));
|
||||
y = -log(fabs(evs[2]));
|
||||
|
||||
if(x > DBL_MAX || y > DBL_MAX) {
|
||||
mpq_abs(tmp, tr);
|
||||
mpq_abs(tmp2, trinv);
|
||||
slope = mpq_log(tmp)/mpq_log(tmp2);
|
||||
} else {
|
||||
slope = y/x;
|
||||
}
|
||||
|
||||
if(slope < 1)
|
||||
slope = 1/slope;
|
||||
|
||||
if(slope > max_slope) {
|
||||
max_slope = slope;
|
||||
max_slope_index = w;
|
||||
}
|
||||
|
||||
if(slope < min_slope) {
|
||||
min_slope = slope;
|
||||
min_slope_index = w;
|
||||
}
|
||||
|
||||
if(mode != 2) {
|
||||
// gmp_printf("%s %.9f %Qd %Qd\n", argv[w+3], slope, tr, trinv);
|
||||
gmp_printf("%s %.9f %.9f %.9f\n", argv[w+3], slope, x, y);
|
||||
}
|
||||
}
|
||||
|
||||
if(mode != 0)
|
||||
printf("%d %.9f %s %d %.9f %s\n",
|
||||
max_slope_index, max_slope, argv[max_slope_index+3],
|
||||
min_slope_index, min_slope, argv[min_slope_index+3]);
|
||||
fflush(stdout);
|
||||
|
||||
mpq_clears(m, t, s, q, tmp, tmp2, tr, trinv, NULL);
|
||||
mat_workspace_clear(ws);
|
||||
for(int i = 0; i < 6; i++)
|
||||
mat_clear(gen[i]);
|
||||
mat_clear(element);
|
||||
mat_clear(inverse);
|
||||
mps_context_free(solver);
|
||||
}
|
||||
Loading…
Reference in New Issue