def compute ( compare , m , n ) : Mo = mat( m , m ) mohanty( compare , Mo , m , n ) print( "mohanty matrix" ) print( show( Mo ) , end = "" ) d = det( Mo , m ) print( "after gaussian elimination" ) print( show( Mo ) , end = "" ) return d
def compute(compare, m, n):
Mo = mat(m, m)
mohanty(compare, Mo, m, n)
print("mohanty matrix")
print(show(Mo), end="")
d = det(Mo, m)
print("after gaussian elimination")
print(show(Mo), end="")
return d
def main ( m , n ) : from matrix import mat , show M = mat( m , n ) info( M , m , n ) print( show( M ) , end = "" )
def main(m, n):
from matrix import mat, show
M = mat(m, n)
partial(M, m, n)
print(show(M), end="")
def compute ( compare , m , n ) : e = tableau( compare , m , n ) print( "count of linear extensions" ) print( show( e ) , end = "" ) return e[m][n]
def main(lines):
from matrix import mat, show, parse
M, m, n = parse(lines)
erase(M, m, n)
print(show(M), end="")
def main ( partial ) : P , m , n = parse( partial ) print( "partial information" ) print( show( P ) , end = "" ) compare = comparator( P ) print( compute( compare , m , n ) )
def main ( partial , total , verbose ) : P , m , n = parse( partial ) if verbose >= 2 : print( "partial information" ) print( show( P ) , end = "" ) T , m , n = parse( total ) oracle = Oracle( T ) if verbose >= 2 : print( "total information" ) print( show( T ) , end = "" ) partial = comparator( P ) e = tableau( partial , m , n ) eP = e[m][n] ITLB = log( eP , 2 ) UB = ITLB / log((1+5**(1/2))/2,2) print( *list( reversed( list( merge( partial , P , oracle , e , m , n , verbose ) ) ) ) , sep = " < " ) if verbose : print( "e(P) :" , eP ) print( "ITLB :" , ITLB ) print( "UB = 1.44.. ITLB :" , UB ) print( "N = total queries :" , len( oracle ) ) print( "N / ITLB :" , len( oracle ) / ITLB ) print( "N / UB :" , len( oracle ) / UB )
def main(lines):
M, m, n = parse(lines)
if n > m:
M = transpose(M, m, n)
reverse(M)
m, n = n, m
print("partial information")
print(show(M), end="")
compare = comparator(M)
print(compute(compare, m, n))
def main ( lines ) : M , m , n = parse( lines ) if n > m : M = transpose( M , m , n ) reverse( M ) m , n = n , m print( "partial information" ) print( show( M ) , end = "" ) compare = comparator( M ) print( compute( compare , m , n ) )
def merge ( partial , P , oracle , e , m , n , verbose = 0 ) : i = m j = n while i > 0 and j > 0 : if verbose >= 2 : callback( "partial information" , i , j ) callback( show( P ) , end = "" ) callback( "tableau" , i , j ) callback( show( e ) , end = "" ) # A_m > B_n if partial( i - 1 , j - 1 ) > 0 : if verbose >= 2 : callback( "I know that A_m > B_n, so I output A_m and decrease m" ) yield "a[%d]" % i i -= 1 # A_m < B_n elif partial( i - 1 , j - 1 ) < 0 : if verbose >= 2 : callback( "I know that A_m < B_n, so I output B_n and decrease n" ) yield "b[%d]" % j j -= 1 # e(P(A_m < B_n)) / e(P) > 2/3 # => # e(P(B_n < A_m)) / e(P) < 1/3 elif 3 * e[i-1][j] < e[i][j] : if verbose >= 2 : callback( "A_m > B_n with probability < 1/3" ) r = j - 1 # By Linial's theorem we are guaranteed to break out this loop. while not e[i][j] <= 3 * e[i][r-1] <= 2 * e[i][j] : r -= 1 if oracle( i - 1 , r - 1 ) < 0 : while j >= r : yield "b[%d]" % j j -= 1 else : P[i-1][r-1] = 1 # update partial information e[i][r] = e[i-1][r] # update lin. ext. count r += 1 while r <= j : e[i][r] = e[i-1][r] + e[i][r-1] # update lin. ext. count r += 1 # e(P(A_m < B_n)) / e(P) < 1/3 elif 3 * e[i][j-1] < e[i][j] : if verbose >= 2 : callback( "A_m < B_n with probability < 1/3" ) r = i - 1 # By Linial's theorem we are guaranteed to break out this loop. while not e[i][j] <= 3 * e[r-1][j] <= 2 * e[i][j] : r -= 1 if oracle( r - 1 , j - 1 ) > 0 : while i >= r : yield "a[%d]" % i i -= 1 else : P[r-1][j-1] = -1 # update partial information e[r][j] = e[r][j-1] # update lin. ext. count r += 1 while r <= i : e[r][j] = e[r][j-1] + e[r-1][j] # update lin. ext. count r += 1 else : # we can simply compare A_m with B_n P[i-1][j-1] = oracle( i - 1 , j - 1 ) while i > 0 : yield "a[%d]" % i i -= 1 while j > 0 : yield "b[%d]" % j j -= 1
def main(m, n):
from matrix import mat, show
M = mat(m, n, 0)
print(show(M), end="")