compute character variety picture based only on billiard words
This commit is contained in:
Florian Stecker
12
.gitignore
vendored
Normal file
12
.gitignore
vendored
Normal file
@@ -0,0 +1,12 @@
|
||||
*.o
|
||||
triangle_group/singular_values
|
||||
.#*
|
||||
singular_values
|
||||
output/
|
||||
special_element
|
||||
max_slope_picture/generate
|
||||
convert
|
||||
billiard_words
|
||||
*.pnm
|
||||
*.png
|
||||
*.hi
|
||||
13
Makefile
13
Makefile
@@ -1,23 +1,26 @@
|
||||
HEADERS=linalg.h mat.h coxeter.h
|
||||
|
||||
#SPECIAL_OPTIONS=-O0 -g -D_DEBUG
|
||||
#SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
|
||||
SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
|
||||
SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
|
||||
#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline
|
||||
#SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -mavx512f -mavx512cd -mavx512er -mavx512pf # KNL
|
||||
#SPECIAL_OPTIONS=
|
||||
|
||||
OPTIONS=-I../mps/include -L../mps/lib -pthread -m64 -std=gnu99 -D_GNU_SOURCE $(SPECIAL_OPTIONS)
|
||||
|
||||
all: singular_values special_element convert
|
||||
all: singular_values special_element convert billiard_words
|
||||
|
||||
convert: convert.hs
|
||||
ghc --make -dynamic convert.hs
|
||||
|
||||
billiard_words: billiard_words.hs
|
||||
ghc --make -dynamic billiard_words.hs
|
||||
|
||||
singular_values: singular_values.o coxeter.o mat.o
|
||||
mpicc $(OPTIONS) -o singular_values coxeter.o singular_values.o mat.o -lm -lgmp -lmps
|
||||
|
||||
special_element: special_element.o coxeter.o linalg.o mat.o
|
||||
gcc $(OPTIONS) -o special_element coxeter.o linalg.o special_element.o mat.o -lm -lgmp -lmps
|
||||
gcc $(OPTIONS) -o special_element coxeter.o linalg.o special_element.o mat.o -lm -lgmp -lmps -lgsl -lcblas
|
||||
|
||||
singular_values.o: singular_values.c $(HEADERS)
|
||||
mpicc $(OPTIONS) -c singular_values.c
|
||||
@@ -35,4 +38,4 @@ mat.o: mat.c $(HEADERS)
|
||||
gcc $(OPTIONS) -c mat.c
|
||||
|
||||
clean:
|
||||
rm -f singular_values special_element coxeter.o linalg.o singular_values.o mat.o special_element.o convert.hi convert.o convert
|
||||
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
|
||||
|
||||
31
billiard_words.hs
Normal file
31
billiard_words.hs
Normal file
@@ -0,0 +1,31 @@
|
||||
import Data.List
|
||||
import Data.Ord
|
||||
import Text.Printf
|
||||
|
||||
main = do
|
||||
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]
|
||||
|
||||
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]
|
||||
where
|
||||
sl ((p,q),_) = fromIntegral p / fromIntegral q
|
||||
|
||||
-- only allows slopes 0 <= p/q <= 1
|
||||
slopeWord :: Int -> Int -> String
|
||||
slopeWord p q =
|
||||
concat $ map word $ zipWith step list (tail list)
|
||||
where
|
||||
p_ = p `div` gcd p q
|
||||
q_ = q `div` gcd p q
|
||||
xmax = if (p_ - q_) `mod` 3 == 0 then q_ else 3*q_
|
||||
list = [(x,y) | x <- ([0..xmax] :: [Int]), let y = floor (fromIntegral x*fromIntegral p/fromIntegral q)]
|
||||
|
||||
step :: (Int,Int) -> (Int,Int) -> (Int,Int)
|
||||
step (x1,y1) (x2,y2) = ((x1-y1) `mod` 3, y2 - y1)
|
||||
|
||||
word :: (Int,Int) -> String
|
||||
word (0,0) = "bc"
|
||||
word (1,0) = "ab"
|
||||
word (2,0) = "ca"
|
||||
word (0,1) = "baca"
|
||||
word (1,1) = "acbc"
|
||||
word (2,1) = "cbab"
|
||||
15
max_slope_picture_billiards/max_slope_highres.plt
Normal file
15
max_slope_picture_billiards/max_slope_highres.plt
Normal file
@@ -0,0 +1,15 @@
|
||||
if(!exists("index")) index = 50
|
||||
|
||||
set xrange [0:0.45]
|
||||
set yrange [0:1]
|
||||
set xyplane at 0
|
||||
#plot "max_slopes_billiard" using 1:2:($3 - 10*floor($3/10)) w p pt 7 ps 1.1 lc palette t ""
|
||||
plot "max_slopes_billiard" using 1:2:3 w p pt 7 ps 1.1 lc palette t ""
|
||||
#splot "max_slopes_billiard" using 1:2:3 w p pt 7 ps 0.3 t ""
|
||||
#plot "max_slopes_billiard" using 1:2:4 w p pt 7 ps 1.1 lc palette t ""
|
||||
|
||||
pause 10
|
||||
#if(MOUSE_KEY == 60) index=index-1
|
||||
#if(MOUSE_KEY == 62) index=index+1
|
||||
#print MOUSE_KEY
|
||||
reread
|
||||
132
max_slope_picture_billiards/words
Normal file
132
max_slope_picture_billiards/words
Normal file
@@ -0,0 +1,132 @@
|
||||
bcabca
|
||||
bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabcabcabcacbcabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabcacbcabcabcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabcacbcabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcacbcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabcacbcabcabcabcabcabcabcabcbabcabcabcabcabcabcabcabacabcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcabacabcabcabcabcabcabcbabcabcabcabcabcabcacbcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcbabcabcabcabcabcabcacbcabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcbabcabcabcabcabcabcacbcabcabcabcabcabcabacabcabcabcabcabcabcbabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcbabcabcabcabcabcabaca
|
||||
bcabcabcabcabcabcbabcabcabcabcabcabacabcabcabcabcabcacbcabcabcabcabcabcbabcabcabcabcabcabaca
|
||||
bcabcabcabcabcacbcabcabcabcabcabcbabcabcabcabcabcabaca
|
||||
bcabcabcabcabcacbcabcabcabcabcabcbabcabcabcabcabcabacabcabcabcabcabaca
|
||||
bcabcabcabcabcacbcabcabcabcabcabcbabcabcabcabcabcbabcabcabcabcabcabacabcabcabcabcabaca
|
||||
bcabcabcabcabaca
|
||||
bcabcabcabcabacabcabcabcabcbabcabcabcabcabcbabcabcabcabcacbcabcabcabcabcacbcabcabcabcabaca
|
||||
bcabcabcabcabacabcabcabcabcbabcabcabcabcabcbabcabcabcabcacbcabcabcabcabaca
|
||||
bcabcabcabcabacabcabcabcabcbabcabcabcabcacbcabcabcabcabaca
|
||||
bcabcabcabcabacabcabcabcabcbabcabcabcabcacbcabcabcabcabacabcabcabcabcbabcabcabcabcacbcabcabcabcabaca
|
||||
bcabcabcabcbabcabcabcabcacbcabcabcabcabaca
|
||||
bcabcabcabcbabcabcabcabcacbcabcabcabcabacabcabcabcabcbabcabcabcabaca
|
||||
bcabcabcabcbabcabcabcabcacbcabcabcabcabacabcabcabcacbcabcabcabcabacabcabcabcabcbabcabcabcabaca
|
||||
bcabcabcabcbabcabcabcabaca
|
||||
bcabcabcabcbabcabcabcabacabcabcabcacbcabcabcabcabacabcabcabcacbcabcabcabcbabcabcabcabaca
|
||||
bcabcabcabcbabcabcabcabacabcabcabcacbcabcabcabcbabcabcabcabaca
|
||||
bcabcabcabcbabcabcabcabacabcabcabcacbcabcabcabcbabcabcabcabacabcabcabcacbcabcabcabcbabcabcabcabaca
|
||||
bcabcabcacbcabcabcabcbabcabcabcabaca
|
||||
bcabcabcacbcabcabcabcbabcabcabcabacabcabcabcacbcabcabcabcbabcabcabcabacabcabcabaca
|
||||
bcabcabcacbcabcabcabcbabcabcabcabacabcabcabaca
|
||||
bcabcabcacbcabcabcabcbabcabcabcbabcabcabcabacabcabcabaca
|
||||
bcabcabcacbcabcabcacbcabcabcabcbabcabcabcbabcabcabcabacabcabcabaca
|
||||
bcabcabcacbcabcabcacbcabcabcabcbabcabcabcbabcabcabcabacabcabcabacabcabcabaca
|
||||
bcabcabcacbcabcabcacbcabcabcabcbabcabcabcbabcabcabcbabcabcabcabacabcabcabacabcabcabaca
|
||||
bcabcabcacbcabcabcacbcabcabcacbcabcabcabcbabcabcabcbabcabcabcbabcabcabcabacabcabcabacabcabcabaca
|
||||
bcabcabaca
|
||||
bcabcabacabcabcabacabcabcabacabcabcbabcabcabcbabcabcabcbabcabcacbcabcabcacbcabcabcacbcabcabaca
|
||||
bcabcabacabcabcabacabcabcbabcabcabcbabcabcabcbabcabcacbcabcabcacbcabcabcacbcabcabaca
|
||||
bcabcabacabcabcabacabcabcbabcabcabcbabcabcabcbabcabcacbcabcabcacbcabcabaca
|
||||
bcabcabacabcabcabacabcabcbabcabcabcbabcabcacbcabcabcacbcabcabaca
|
||||
bcabcabacabcabcbabcabcabcbabcabcacbcabcabcacbcabcabaca
|
||||
bcabcabacabcabcbabcabcabcbabcabcacbcabcabcacbcabcabacabcabcabacabcabcbabcabcabcbabcabcacbcabcabaca
|
||||
bcabcabacabcabcbabcabcabcbabcabcacbcabcabaca
|
||||
bcabcabacabcabcbabcabcacbcabcabcacbcabcabacabcabcbabcabcabcbabcabcacbcabcabaca
|
||||
bcabcabacabcabcbabcabcacbcabcabaca
|
||||
bcabcabacabcabcbabcabcacbcabcabacabcabcbabcabcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabaca
|
||||
bcabcabacabcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabaca
|
||||
bcabcabacabcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabaca
|
||||
bcabcbabcabcacbcabcabaca
|
||||
bcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabacabcabcbabcabaca
|
||||
bcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabacabcabcbabcabaca
|
||||
bcabcbabcabcacbcabcabacabcabcbabcabcacbcabcabacabcacbcabcabacabcabcbabcabcacbcabcabacabcabcbabcabaca
|
||||
bcabcbabcabcacbcabcabacabcabcbabcabaca
|
||||
bcabcbabcabcacbcabcabacabcacbcabcabacabcabcbabcabcacbcabcbabcabcacbcabcabacabcabcbabcabaca
|
||||
bcabcbabcabcacbcabcabacabcacbcabcabacabcabcbabcabaca
|
||||
bcabcbabcabcacbcabcbabcabcacbcabcabacabcacbcabcabacabcabcbabcabaca
|
||||
bcabcbabcabcacbcabcbabcabcacbcabcabacabcacbcabcabacabcabcbabcabacabcabcbabcabaca
|
||||
bcabcbabcabcacbcabcbabcabcacbcabcabacabcacbcabcabacabcacbcabcabacabcabcbabcabacabcabcbabcabaca
|
||||
bcabcbabcabaca
|
||||
bcabcbabcabacabcabcbabcabacabcacbcabcabacabcacbcabcabacabcacbcabcbabcabcacbcabcbabcabaca
|
||||
bcabcbabcabacabcabcbabcabacabcacbcabcabacabcacbcabcbabcabcacbcabcbabcabaca
|
||||
bcabcbabcabacabcacbcabcabacabcacbcabcbabcabcacbcabcbabcabaca
|
||||
bcabcbabcabacabcacbcabcabacabcacbcabcbabcabaca
|
||||
bcabcbabcabacabcacbcabcbabcabcacbcabcbabcabacabcacbcabcabacabcacbcabcbabcabaca
|
||||
bcabcbabcabacabcacbcabcbabcabaca
|
||||
bcabcbabcabacabcacbcabcbabcabacabcacbcabcabacabcacbcabcbabcabacabcacbcabcbabcabaca
|
||||
bcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabaca
|
||||
bcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabaca
|
||||
bcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabaca
|
||||
bcacbcabcbabcabaca
|
||||
bcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabaca
|
||||
bcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabaca
|
||||
bcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabaca
|
||||
bcacbcabcbabcabacabcacbcabcbabcabacabcacbcabcbabcbabcabacabcacbcabcbabcabacabcacbcabcbabcabacabaca
|
||||
bcacbcabcbabcabacabcacbcabcbabcabacabaca
|
||||
bcacbcabcbabcabacabcacbcabcbabcbabcabacabcacbcabcbabcabacabaca
|
||||
bcacbcabcbabcabacabcacbcacbcabcbabcabacabcacbcabcbabcbabcabacabcacbcabcbabcabacabaca
|
||||
bcacbcabcbabcabacabaca
|
||||
bcacbcabcbabcabacabacabcacbcabcbabcbabcabacabcacbcabcbabcbabcabacabcacbcacbcabcbabcabacabaca
|
||||
bcacbcabcbabcabacabacabcacbcabcbabcbabcabacabcacbcacbcabcbabcabacabaca
|
||||
bcacbcabcbabcbabcabacabcacbcacbcabcbabcabacabaca
|
||||
bcacbcabcbabcbabcabacabcacbcacbcabcbabcabacabacabcacbcabcbabcbabcabacabaca
|
||||
bcacbcabcbabcbabcabacabcacbcacbcabcbabcabacabacabcacbcacbcabcbabcabacabacabcacbcabcbabcbabcabacabaca
|
||||
bcacbcabcbabcbabcabacabaca
|
||||
bcacbcabcbabcbabcabacabacabcacbcacbcabcbabcabacabacabcacbcacbcabcbabcbabcabacabaca
|
||||
bcacbcabcbabcbabcabacabacabcacbcacbcabcbabcbabcabacabaca
|
||||
bcacbcabcbabcbabcabacabacabcacbcacbcabcbabcbabcabacabacabcacbcacbcabcbabcbabcabacabaca
|
||||
bcacbcacbcabcbabcbabcabacabaca
|
||||
bcacbcacbcabcbabcbabcabacabacabcacbcacbcabcbabcbabcabacabacabcacbcacbcabcbabcbabcabacabacabaca
|
||||
bcacbcacbcabcbabcbabcabacabacabcacbcacbcabcbabcbabcabacabacabaca
|
||||
bcacbcacbcabcbabcbabcabacabacabcacbcacbcabcbabcbabcbabcabacabacabcacbcacbcabcbabcbabcabacabacabaca
|
||||
bcacbcacbcabcbabcbabcabacabacabaca
|
||||
bcacbcacbcabcbabcbabcbabcabacabacabcacbcacbcacbcabcbabcbabcabacabacabaca
|
||||
bcacbcacbcabcbabcbabcbabcabacabacabaca
|
||||
bcacbcacbcabcbabcbabcbabcabacabacabacabcacbcacbcacbcabcbabcbabcbabcabacabacabaca
|
||||
bcacbcacbcacbcabcbabcbabcbabcabacabacabaca
|
||||
bcacbcacbcacbcabcbabcbabcbabcabacabacabacabcacbcacbcacbcabcbabcbabcbabcabacabacabacabaca
|
||||
bcacbcacbcacbcabcbabcbabcbabcabacabacabacabaca
|
||||
bcacbcacbcacbcabcbabcbabcbabcbabcabacabacabacabcacbcacbcacbcacbcabcbabcbabcbabcabacabacabacabaca
|
||||
bcacbcacbcacbcabcbabcbabcbabcbabcabacabacabacabaca
|
||||
bcacbcacbcacbcacbcabcbabcbabcbabcbabcabacabacabacabaca
|
||||
bcacbcacbcacbcacbcabcbabcbabcbabcbabcabacabacabacabacabaca
|
||||
bcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcabacabacabacabacabaca
|
||||
bcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcabacabacabacabacabaca
|
||||
bcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcabacabacabacabacabacabaca
|
||||
bcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcbabcabacabacabacabacabacabaca
|
||||
bcacbcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcbabcabacabacabacabacabacabaca
|
||||
bcacbcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcbabcabacabacabacabacabacabacabaca
|
||||
bcacbcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcbabcbabcabacabacabacabacabacabacabaca
|
||||
bcacbcacbcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcbabcbabcabacabacabacabacabacabacabaca
|
||||
bcacbcacbcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcbabcbabcabacabacabacabacabacabacabacabaca
|
||||
bcacbcacbcacbcacbcacbcacbcacbcabcbabcbabcbabcbabcbabcbabcbabcbabcabacabacabacabacabacabacabacabaca
|
||||
baca
|
||||
|
||||
@@ -8,6 +8,11 @@
|
||||
|
||||
#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
|
||||
#define DEBUG(msg, ...)
|
||||
#define DENOMINATOR 300
|
||||
#define WIDTH 135
|
||||
#define STARTX 121
|
||||
#define HEIGHT 300
|
||||
#define IDX(i,j) (((i)-1)*HEIGHT + ((j)-1))
|
||||
|
||||
int solve_characteristic_polynomial(mps_context *solv, mpq_t tr, mpq_t trinv, double *eigenvalues)
|
||||
{
|
||||
@@ -189,10 +194,12 @@ int main(int argc, char *argv[])
|
||||
mat element, inverse;
|
||||
int letter1, letter2, letter;
|
||||
mpq_t tr, trinv;
|
||||
double x, y;
|
||||
double x, y, slope;
|
||||
int retval;
|
||||
double evs[3];
|
||||
char buf[100];
|
||||
double *max_slope;
|
||||
int *max_slope_index;
|
||||
|
||||
DEBUG("Allocate\n");
|
||||
|
||||
@@ -202,68 +209,83 @@ int main(int argc, char *argv[])
|
||||
mat_init(gen[i], 3);
|
||||
mat_init(element, 3);
|
||||
mat_init(inverse, 3);
|
||||
max_slope = malloc(sizeof(double)*WIDTH*HEIGHT);
|
||||
max_slope_index = malloc(sizeof(int)*WIDTH*HEIGHT);
|
||||
memset(max_slope_index, 0, sizeof(int)*WIDTH*HEIGHT);
|
||||
memset(max_slope, 0, sizeof(int)*WIDTH*HEIGHT);
|
||||
|
||||
solver = mps_context_new();
|
||||
mps_context_set_output_prec(solver, 20); // relative precision
|
||||
mps_context_set_output_goal(solver, MPS_OUTPUT_GOAL_APPROXIMATE);
|
||||
|
||||
for(int i = 1; i <= 99; i++) {
|
||||
for(int j = 1; j <= 100; j++) {
|
||||
mpq_set_ui(t, j, 100);
|
||||
mpq_set_ui(m, i, 100); // 414/1000 ~ sqrt(2)-1 <-> s=1
|
||||
s = (1-mpq_get_d(m)*mpq_get_d(m))/(2*mpq_get_d(m));
|
||||
for(int i = STARTX; i <= WIDTH; i++) {
|
||||
for(int j = 1; j <= HEIGHT; j++) {
|
||||
for(int w = 1; w < argc; w++) {
|
||||
mpq_set_ui(t, j, DENOMINATOR);
|
||||
mpq_set_ui(m, i, DENOMINATOR); // 414/1000 ~ sqrt(2)-1 <-> s=1
|
||||
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);
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user