compute character variety picture based only on billiard words
This commit is contained in:
Florian Stecker
parent
c2c3f24854
commit
67e5b30808
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@ -0,0 +1,12 @@
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*.o
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triangle_group/singular_values
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.#*
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singular_values
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output/
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special_element
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max_slope_picture/generate
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convert
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billiard_words
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*.pnm
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*.png
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*.hi
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13
Makefile
13
Makefile
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@ -1,23 +1,26 @@
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HEADERS=linalg.h mat.h coxeter.h
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#SPECIAL_OPTIONS=-O0 -g -D_DEBUG
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#SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
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SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
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SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
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#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
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#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -mavx512f -mavx512cd -mavx512er -mavx512pf # KNL
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#SPECIAL_OPTIONS=
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OPTIONS=-I../mps/include -L../mps/lib -pthread -m64 -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS)
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all: singular_values special_element convert
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all: singular_values special_element convert billiard_words
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convert: convert.hs
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ghc --make -dynamic convert.hs
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billiard_words: billiard_words.hs
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ghc --make -dynamic billiard_words.hs
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singular_values: singular_values.o coxeter.o mat.o
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mpicc $(OPTIONS) -o singular_values coxeter.o singular_values.o mat.o -lm -lgmp -lmps
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special_element: special_element.o coxeter.o linalg.o mat.o
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gcc $(OPTIONS) -o special_element coxeter.o linalg.o special_element.o mat.o -lm -lgmp -lmps
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gcc $(OPTIONS) -o special_element coxeter.o linalg.o special_element.o mat.o -lm -lgmp -lmps -lgsl -lcblas
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singular_values.o: singular_values.c $(HEADERS)
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mpicc $(OPTIONS) -c singular_values.c
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@ -35,4 +38,4 @@ mat.o: mat.c $(HEADERS)
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gcc $(OPTIONS) -c mat.c
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clean:
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rm -f singular_values special_element coxeter.o linalg.o singular_values.o mat.o special_element.o convert.hi convert.o convert
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rm -f singular_values special_element coxeter.o linalg.o singular_values.o mat.o special_element.o convert.hi convert.o convert billiard_words.hi billiard_words.o billiard_words
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@ -0,0 +1,31 @@
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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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main = do
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putStrLn $ unlines [printf "%d/%d\t%.5f\t%.5f\t%d\t%s" p q (fromIntegral p / fromIntegral q :: Double) (sqrt 3 / (1 + 2*fromIntegral q/fromIntegral p) :: Double) (length w) w | ((p,q),w) <- wordlist, length w <= 100]
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wordlist = nub $ sortBy (comparing sl) [((p `div` gcd p q, q `div` gcd p q), slopeWord p q) | p <- [0..50], q <- [1..50], p <= q]
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where
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sl ((p,q),_) = fromIntegral p / fromIntegral q
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-- only allows slopes 0 <= p/q <= 1
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slopeWord :: Int -> Int -> String
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slopeWord p q =
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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_
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list = [(x,y) | x <- ([0..xmax] :: [Int]), let y = floor (fromIntegral x*fromIntegral p/fromIntegral q)]
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step :: (Int,Int) -> (Int,Int) -> (Int,Int)
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step (x1,y1) (x2,y2) = ((x1-y1) `mod` 3, y2 - y1)
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word :: (Int,Int) -> String
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word (0,0) = "bc"
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word (1,0) = "ab"
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word (2,0) = "ca"
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word (0,1) = "baca"
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word (1,1) = "acbc"
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word (2,1) = "cbab"
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@ -0,0 +1,15 @@
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if(!exists("index")) index = 50
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set xrange [0:0.45]
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set yrange [0:1]
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set xyplane at 0
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#plot "max_slopes_billiard" using 1:2:($3 - 10*floor($3/10)) w p pt 7 ps 1.1 lc palette t ""
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plot "max_slopes_billiard" using 1:2:3 w p pt 7 ps 1.1 lc palette t ""
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#splot "max_slopes_billiard" using 1:2:3 w p pt 7 ps 0.3 t ""
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#plot "max_slopes_billiard" using 1:2:4 w p pt 7 ps 1.1 lc palette t ""
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pause 10
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#if(MOUSE_KEY == 60) index=index-1
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#if(MOUSE_KEY == 62) index=index+1
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#print MOUSE_KEY
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reread
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bcabca
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bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabcabcabcacbcabcabcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcabcacbcabcabcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabcacbcabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcacbcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabcacbcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabacabcabcabcabcabcabcabaca
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bcabcabcabcabcabcabaca
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bcabcabcabcabcabcabacabcabcabcabcabcabcbabcabcabcabcabcabcacbcabcabcabcabcabcabaca
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bcabcabcabcabcabcbabcabcabcabcabcabcacbcabcabcabcabcabcabaca
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bcabcabcabcabcabcbabcabcabcabcabcabcacbcabcabcabcabcabcabacabcabcabcabcabcabcbabcabcabcabcabcabaca
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bcabcabcabcabcabcbabcabcabcabcabcabaca
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bcabcabcabcabcabcbabcabcabcabcabcabacabcabcabcabcabcacbcabcabcabcabcabcbabcabcabcabcabcabaca
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bcabcabcabcabcacbcabcabcabcabcabcbabcabcabcabcabcabaca
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bcabcabcabcabcacbcabcabcabcabcabcbabcabcabcabcabcabacabcabcabcabcabaca
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bcabcabcabcabcacbcabcabcabcabcabcbabcabcabcabcabcbabcabcabcabcabcabacabcabcabcabcabaca
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bcabcabcabcabaca
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bcabcabcabcabacabcabcabcabcbabcabcabcabcabcbabcabcabcabcacbcabcabcabcabcacbcabcabcabcabaca
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bcabcabcabcabacabcabcabcabcbabcabcabcabcabcbabcabcabcabcacbcabcabcabcabaca
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bcabcabcabcabacabcabcabcabcbabcabcabcabcacbcabcabcabcabaca
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bcabcabcabcabacabcabcabcabcbabcabcabcabcacbcabcabcabcabacabcabcabcabcbabcabcabcabcacbcabcabcabcabaca
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bcabcabcabcbabcabcabcabcacbcabcabcabcabaca
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bcabcabcabcbabcabcabcabcacbcabcabcabcabacabcabcabcabcbabcabcabcabaca
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bcabcabcabcbabcabcabcabcacbcabcabcabcabacabcabcabcacbcabcabcabcabacabcabcabcabcbabcabcabcabaca
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bcabcabcabcbabcabcabcabaca
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bcabcabcabcbabcabcabcabacabcabcabcacbcabcabcabcabacabcabcabcacbcabcabcabcbabcabcabcabaca
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bcabcabcabcbabcabcabcabacabcabcabcacbcabcabcabcbabcabcabcabaca
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bcabcabcabcbabcabcabcabacabcabcabcacbcabcabcabcbabcabcabcabacabcabcabcacbcabcabcabcbabcabcabcabaca
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bcabcabcacbcabcabcabcbabcabcabcabaca
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bcabcabcacbcabcabcabcbabcabcabcabacabcabcabcacbcabcabcabcbabcabcabcabacabcabcabaca
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bcabcabcacbcabcabcabcbabcabcabcabacabcabcabaca
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bcabcabcacbcabcabcabcbabcabcabcbabcabcabcabacabcabcabaca
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bcabcabcacbcabcabcacbcabcabcabcbabcabcabcbabcabcabcabacabcabcabaca
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bcabcabcacbcabcabcacbcabcabcabcbabcabcabcbabcabcabcabacabcabcabacabcabcabaca
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bcabcabcacbcabcabcacbcabcabcabcbabcabcabcbabcabcabcbabcabcabcabacabcabcabacabcabcabaca
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bcabcabcacbcabcabcacbcabcabcacbcabcabcabcbabcabcabcbabcabcabcbabcabcabcabacabcabcabacabcabcabaca
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bcabcabaca
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bcabcabacabcabcabacabcabcabacabcabcbabcabcabcbabcabcabcbabcabcacbcabcabcacbcabcabcacbcabcabaca
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bcabcabacabcabcabacabcabcbabcabcabcbabcabcabcbabcabcacbcabcabcacbcabcabcacbcabcabaca
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bcabcabacabcabcabacabcabcbabcabcabcbabcabcabcbabcabcacbcabcabcacbcabcabaca
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bcabcabacabcabcabacabcabcbabcabcabcbabcabcacbcabcabcacbcabcabaca
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bcabcabacabcabcbabcabcabcbabcabcacbcabcabcacbcabcabaca
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bcabcabacabcabcbabcabcabcbabcabcacbcabcabcacbcabcabacabcabcabacabcabcbabcabcabcbabcabcacbcabcabaca
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bcabcabacabcabcbabcabcabcbabcabcacbcabcabaca
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bcabcabacabcabcbabcabcacbcabcabcacbcabcabacabcabcbabcabcabcbabcabcacbcabcabaca
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bcabcabacabcabcbabcabcacbcabcabaca
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bcabcabacabcabcbabcabcacbcabcabacabcabcbabcabcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabaca
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bcabcabacabcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabaca
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bcabcabacabcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabaca
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bcabcbabcabcacbcabcabaca
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bcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabacabcabcbabcabaca
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bcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabacabcabcbabcabaca
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bcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabacabcacbcabcabacabcabcbabcabcacbcabcabacabcabcbabcabaca
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bcabcbabcabcacbcabcabacabcabcbabcabaca
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bcabcbabcabcacbcabcabacabcacbcabcabacabcabcbabcabcacbcabcbabcabcacbcabcabacabcabcbabcabaca
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bcabcbabcabcacbcabcabacabcacbcabcabacabcabcbabcabaca
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bcabcbabcabcacbcabcbabcabcacbcabcabacabcacbcabcabacabcabcbabcabaca
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bcabcbabcabcacbcabcbabcabcacbcabcabacabcacbcabcabacabcabcbabcabacabcabcbabcabaca
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bcabcbabcabcacbcabcbabcabcacbcabcabacabcacbcabcabacabcacbcabcabacabcabcbabcabacabcabcbabcabaca
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bcabcbabcabaca
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bcabcbabcabacabcabcbabcabacabcacbcabcabacabcacbcabcabacabcacbcabcbabcabcacbcabcbabcabaca
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bcabcbabcabacabcabcbabcabacabcacbcabcabacabcacbcabcbabcabcacbcabcbabcabaca
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bcabcbabcabacabcacbcabcabacabcacbcabcbabcabcacbcabcbabcabaca
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bcabcbabcabacabcacbcabcabacabcacbcabcbabcabaca
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bcabcbabcabacabcacbcabcbabcabcacbcabcbabcabacabcacbcabcabacabcacbcabcbabcabaca
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bcabcbabcabacabcacbcabcbabcabaca
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bcabcbabcabacabcacbcabcbabcabacabcacbcabcabacabcacbcabcbabcabacabcacbcabcbabcabaca
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bcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabaca
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bcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabaca
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bcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabaca
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bcacbcabcbabcabaca
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bcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabaca
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bcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabaca
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bcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabaca
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bcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabaca
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bcacbcabcbabcabacabcacbcabcbabcabacabaca
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bcacbcabcbabcabacabcacbcabcbabcbabcabacabcacbcabcbabcabacabaca
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bcacbcabcbabcabacabcacbcacbcabcbabcabacabcacbcabcbabcbabcabacabcacbcabcbabcabacabaca
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bcacbcabcbabcabacabaca
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bcacbcabcbabcabacabacabcacbcabcbabcbabcabacabcacbcabcbabcbabcabacabcacbcacbcabcbabcabacabaca
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bcacbcabcbabcabacabacabcacbcabcbabcbabcabacabcacbcacbcabcbabcabacabaca
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bcacbcabcbabcbabcabacabcacbcacbcabcbabcabacabaca
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bcacbcabcbabcbabcabacabcacbcacbcabcbabcabacabacabcacbcabcbabcbabcabacabaca
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bcacbcabcbabcbabcabacabcacbcacbcabcbabcabacabacabcacbcacbcabcbabcabacabacabcacbcabcbabcbabcabacabaca
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bcacbcabcbabcbabcabacabaca
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bcacbcabcbabcbabcabacabacabcacbcacbcabcbabcabacabacabcacbcacbcabcbabcbabcabacabaca
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bcacbcabcbabcbabcabacabacabcacbcacbcabcbabcbabcabacabaca
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bcacbcabcbabcbabcabacabacabcacbcacbcabcbabcbabcabacabacabcacbcacbcabcbabcbabcabacabaca
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bcacbcacbcabcbabcbabcabacabaca
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bcacbcacbcabcbabcbabcabacabacabcacbcacbcabcbabcbabcabacabacabcacbcacbcabcbabcbabcabacabacabaca
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bcacbcacbcabcbabcbabcabacabacabcacbcacbcabcbabcbabcabacabacabaca
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bcacbcacbcabcbabcbabcabacabacabcacbcacbcabcbabcbabcbabcabacabacabcacbcacbcabcbabcbabcabacabacabaca
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bcacbcacbcabcbabcbabcabacabacabaca
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bcacbcacbcabcbabcbabcbabcabacabacabcacbcacbcacbcabcbabcbabcabacabacabaca
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bcacbcacbcabcbabcbabcbabcabacabacabaca
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bcacbcacbcabcbabcbabcbabcabacabacabacabcacbcacbcacbcabcbabcbabcbabcabacabacabaca
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bcacbcacbcacbcabcbabcbabcbabcabacabacabaca
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bcacbcacbcacbcabcbabcbabcbabcabacabacabacabcacbcacbcacbcabcbabcbabcbabcabacabacabacabaca
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bcacbcacbcacbcabcbabcbabcbabcabacabacabacabaca
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bcacbcacbcacbcabcbabcbabcbabcbabcabacabacabacabcacbcacbcacbcacbcabcbabcbabcbabcabacabacabacabaca
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bcacbcacbcacbcabcbabcbabcbabcbabcabacabacabacabaca
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bcacbcacbcacbcacbcabcbabcbabcbabcbabcabacabacabacabaca
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bcacbcacbcacbcacbcabcbabcbabcbabcbabcabacabacabacabacabaca
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bcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcabacabacabacabacabaca
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bcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcabacabacabacabacabaca
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bcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcabacabacabacabacabacabaca
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bcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcbabcabacabacabacabacabacabaca
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bcacbcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcbabcabacabacabacabacabacabaca
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bcacbcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcbabcabacabacabacabacabacabacabaca
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bcacbcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcbabcbabcabacabacabacabacabacabacabaca
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bcacbcacbcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcbabcbabcabacabacabacabacabacabacabaca
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bcacbcacbcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcbabcbabcabacabacabacabacabacabacabacabaca
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bcacbcacbcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcbabcbabcbabcabacabacabacabacabacabacabacabaca
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baca
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@ -8,6 +8,11 @@
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#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
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#define DEBUG(msg, ...)
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#define DENOMINATOR 300
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#define WIDTH 135
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#define STARTX 121
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#define HEIGHT 300
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#define IDX(i,j) (((i)-1)*HEIGHT + ((j)-1))
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int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues)
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{
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@ -189,10 +194,12 @@ int main(int argc, char *argv[])
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mat element, inverse;
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int letter1, letter2, letter;
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mpq_t tr, trinv;
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double x, y;
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double x, y, slope;
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int retval;
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double evs[3];
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char buf[100];
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double *max_slope;
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int *max_slope_index;
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DEBUG("Allocate\n");
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@ -202,68 +209,83 @@ int main(int argc, char *argv[])
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mat_init(gen[i], 3);
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mat_init(element, 3);
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mat_init(inverse, 3);
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max_slope = malloc(sizeof(double)*WIDTH*HEIGHT);
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max_slope_index = malloc(sizeof(int)*WIDTH*HEIGHT);
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memset(max_slope_index, 0, sizeof(int)*WIDTH*HEIGHT);
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memset(max_slope, 0, sizeof(int)*WIDTH*HEIGHT);
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solver = mps_context_new();
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mps_context_set_output_prec(solver, 20); // relative precision
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mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
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for(int i = 1; i <= 99; i++) {
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for(int j = 1; j <= 100; j++) {
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mpq_set_ui(t, j, 100);
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mpq_set_ui(m, i, 100); // 414/1000 ~ sqrt(2)-1 <-> s=1
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s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m));
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for(int i = STARTX; i <= WIDTH; i++) {
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for(int j = 1; j <= HEIGHT; j++) {
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for(int w = 1; w < argc; w++) {
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mpq_set_ui(t, j, DENOMINATOR);
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mpq_set_ui(m, i, DENOMINATOR); // 414/1000 ~ sqrt(2)-1 <-> s=1
|
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s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m));
|
||||
|
||||
DEBUG("Compute matrix\n");
|
||||
initialize_triangle_generators(ws, gen, m, t);
|
||||
DEBUG("Compute matrix\n");
|
||||
initialize_triangle_generators(ws, gen, m, t);
|
||||
|
||||
mat_identity(element);
|
||||
mat_identity(inverse);
|
||||
for(int i = 0; i < strlen(argv[1]); i+=2) {
|
||||
letter1 = argv[1][i] - 'a';
|
||||
letter2 = argv[1][i+1] - 'a';
|
||||
mat_identity(element);
|
||||
mat_identity(inverse);
|
||||
for(int k = 0; k < strlen(argv[w]); k+=2) {
|
||||
letter1 = argv[w][k] - 'a';
|
||||
letter2 = argv[w][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
|
||||
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_multiply(ws, element, element, gen[letter]);
|
||||
mat_multiply(ws, inverse, gen[(letter+3)%6], inverse);
|
||||
}
|
||||
|
||||
DEBUG("Compute traces\n");
|
||||
DEBUG("Compute traces\n");
|
||||
|
||||
mat_trace(tr, element);
|
||||
mat_trace(trinv, inverse);
|
||||
mat_trace(tr, element);
|
||||
mat_trace(trinv, inverse);
|
||||
|
||||
DEBUG("Solve characteristic polynomials\n");
|
||||
retval = solve_characteristic_polynomial(solver, tr, trinv, evs);
|
||||
if(retval == 1) {
|
||||
fprintf(stderr, "Error! Could not solve polynomial.\n");
|
||||
return 1;
|
||||
}
|
||||
DEBUG("Solve characteristic polynomials\n");
|
||||
retval = solve_characteristic_polynomial(solver, 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]);
|
||||
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]));
|
||||
x = log(fabs(evs[0]));
|
||||
y = -log(fabs(evs[2]));
|
||||
slope = y/x > 1 ? y/x : x/y;
|
||||
|
||||
if(slope > max_slope[IDX(i,j)]) {
|
||||
max_slope[IDX(i,j)] = slope;
|
||||
max_slope_index[IDX(i,j)] = w;
|
||||
}
|
||||
|
||||
// gmp_printf("%Qd %Qd %f %f %f\n", tr, trinv, x, y, y/x);
|
||||
gmp_printf("%.5f %.5f %.7f %.9f\n", mpq_get_d(t), mpq_get_d(m), s, y/x);
|
||||
// gmp_printf("%.5f %.5f %.7f %.9f\n", mpq_get_d(t), mpq_get_d(m), s, slope);
|
||||
|
||||
}
|
||||
|
||||
printf("%.5f %.5f %d %.9f\n", (double)i/DENOMINATOR, (double)j/DENOMINATOR, max_slope_index[IDX(i,j)], max_slope[IDX(i,j)]);
|
||||
fflush(stdout);
|
||||
}
|
||||
}
|
||||
|
||||
|
|
@ -275,4 +297,6 @@ int main(int argc, char *argv[])
|
|||
mat_clear(element);
|
||||
mat_clear(inverse);
|
||||
mps_context_free(solver);
|
||||
free(max_slope);
|
||||
free(max_slope_index);
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue