require "complex"
require "matrix"

local function isnormal(m, tol = 1e-14)
    local m1 = m:conjtranspose():matmul(m)
    local m2 = m:matmul(m:conjtranspose())
    return m1:same(m2, tol)
end

local function isunitary(m, tol = 1e-14)
    return m:inverse():same(m:conjtranspose(), tol)
end

local zero = complex.of(0)
local one  = complex.of(1)
local x = math.sqrt(2) / 2
local f = |e|-> e:format("%5.3f")

local cm1 = matrix.from({
    {complex.of(3), complex.of(2, 1)},
    {complex.of(2, -1), complex.of(1)}
}, zero)

local cm2 = matrix.from({
    {one,  one,  zero},
    {zero, one,  one},
    {one,  zero, one}
}, zero)

local cm3 = matrix.from({
    {complex.of(x), complex.of(x), zero},
    {complex.of(0, -x), complex.of(0, x), zero},
    {zero, zero, complex.of(0, 1)}
}, zero)

for {cm1, cm2, cm3} as cm do
    print("Matrix: ")
    print(cm:mapped(f))
    print("\nConjugate transpose:")
    print(cm:conjtranspose():mapped(f))
    print($"\nHermitian : {cm:ishermitian()}")
    print($"Normal    : {isnormal(cm)}")
    print($"Unitary   : {isunitary(cm)}")
    print()
end