# spectral-norm Ruby #4 program

## source code

```# The Computer Language Benchmarks Game
# https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
# Contributed by Sokolov Yura
# Modified by Chris Houhoulis (April 2013):
#   - made loops uglier to avoid the unnecessary overhead of blocks
#   - nicer naming for readability

ARRAY_LENGTH = ARGV.to_i

u = Array.new(ARRAY_LENGTH, 1)
v = []

def eval_A(i,j)
1.0/((i+j)*(i+j+1)/2+i+1)
end

def vector_times_array(vector)
arr, i = [], 0
while i < ARRAY_LENGTH
sum, j = 0, 0
while j < ARRAY_LENGTH
sum += eval_A(i,j) * vector[j]
j += 1
end
arr << sum
i += 1
end
arr
end

def vector_times_array_transposed(vector)
arr, i = [], 0
while i < ARRAY_LENGTH
sum, j = 0, 0
while j < ARRAY_LENGTH
sum += eval_A(j,i) * vector[j]
j += 1
end
arr << sum
i += 1
end
arr
end

def vector_times_array_times_array_transposed(vector)
vector_times_array_transposed(vector_times_array(vector))
end

10.times do
v = vector_times_array_times_array_transposed(u)
u = vector_times_array_times_array_transposed(v)
end

vBv, vv, i = 0, 0, 0
while i < ARRAY_LENGTH
vBv += u[i]*v[i]
vv += v[i]*v[i]
i += 1
end

print "%0.9f" % (Math.sqrt(vBv/vv)), "\n"
```

## notes, command-line, and program output

```NOTES: