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# The Computer Language Shootout
# http://shootout.alioth.debian.org/
# Contributed by Sokolov Yura
def eval_A(i,j)
return 1.0/((i+j)*(i+j+1)/2+i+1)
end
def eval_A_times_u(u)
v, i = nil, nil
(0..u.length-1).collect { |i|
v = 0
for j in 0..u.length-1
v += eval_A(i,j)*u[j]
end
v
}
end
def eval_At_times_u(u)
v, i = nil, nil
(0..u.length-1).collect{|i|
v = 0
for j in 0..u.length-1
v += eval_A(j,i)*u[j]
end
v
}
end
def eval_AtA_times_u(u)
return eval_At_times_u(eval_A_times_u(u))
end
n = 500 # ARGV[0].to_i
u=[1]*n
for i in 1..10
v=eval_AtA_times_u(u)
u=eval_AtA_times_u(v)
end
vBv=0
vv=0
for i in 0..n-1
vBv += u[i]*v[i]
vv += v[i]*v[i]
end
str = "%0.9f" % (Math.sqrt(vBv/vv)), "\n"
# print str
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